What I've done in my Hoard of the Dragon Queen Campaign is to have "the local clerics/priests" resurrect dead characters in exchange for the assistance the party is providing the town. So, if your characters are helping the city (I haven't read the starter set, avoiding spoilers), then local authorities could provide healing in exchange. This means, however, that the character has to sit out the next mission (so, they'll have to roll a temp or something--temp could be a generic NPC, like a soldier from the local militia, sent to help the party; or they could roll another character, though it has to be a different race and class than the one that died).
If they actually have the resources to pay for the spell (as per the Starter Set Guidelines), then the character doesn't have to sit out. I think it's a fair 'penalty' without trivializing death.
More specifically, Neverwinter has traditionally been one of the largest (if not the largest) cities in the Sword Coast--undoubtedly such a service is available. The cost would be at least 500 gp, given the material components required to cast Raise Dead.
Then again, the city was presumably destroyed in the 4E lore; without having read the starter set info (I don't want to spoil it), I'm not sure about the current state of the city. This wouldn't be a random NPC; however, it need not be a "high-level cleric--" a L9 Cleric can cast Raise Dead.
About hiring spellcasters, from the PHB, p. 159:
Hiring someone to cast a relatively common spell of 1st or 2nd level, such as cure wounds or identify, is easy enough in a city or town, and might cost 10 to 50 gold pieces (plus the cost of any expensive material components). Finding someone able and willing to cast a higher-level spell might involve traveling to a large city, perhaps one with a university or prominent temple. Once found, the spellcaster might ask for a service instead of payment— the kind of service that only adventurers can provide, such as retrieving a rare item from a dangerous locale or traversing a monster- infested wilderness to deliver something important to a distant settlement.
Rangers Don't Get Foci
All classes that use a focus have a "Spellcasting Focus" subheading to their Spellcasting (or Warlock) feature:
- Wizard (arcane focus)
- Warlock (arcane focus)
- Sorcerer (arcane focus)
- Paladin (holy symbol)
- Druid (druidic focus)
- Cleric (holy symbol)
- Bard (musical instrument)
The wizards feature for instance reads:
SPELLCASTING FOCUS
You can use an arcane focus (found in chapter 5) as a
spellcasting focus for your wizard spells.
PHB 114
With the exception of the Ranger and Eldritch Knight, which specifically don't mention foci as part of the spell casting feature. Who have no such text.
It Is Intentional
Jeremy Crawford clarified in a tweet that the omission of focus for the ranger class is intentional. He was asked:
[D]o rangers use spellcasting foci, and/or do they need to buy component pouches at 2nd level?
And replied:
The ranger doesn't have a spellcasting focus. The trusty component pouch will do the job.
https://twitter.com/JeremyECrawford/status/687417277231267844?ref_src=twsrc%5Etfw
This makes sense as most rangers would likely have a bow. All bows, even the hand cross bow (even with Crossbow Expert), requires a free hand to load. So holding a focus would mess with the traditional ranger with bow. You keep a free hand for spells, pouch and loading firing arrows.
Mechanically
Using a bow, you have the weapon in one hand and the other on string. After you fire, your hand is free again. When you cast you pull out the components and put them back, or they are consumed, and your hand is free again. Works great with a bow. However, the arcane and druidic focus require object iterations, and you either have to drop it or spend the book keeping at the start and end of each turn.
Yes, a holy symbol could be worn and keep the hands free, likely why they did that for paladins, but they chose to go a different direction with the ranger.
Thematically
Ranger forage for food and materials, they are self reliant. It isn't hard to see them restocking their component pouch as they move through the wild area.
What about the Mistletoe?
it might be impossible to find mistletoe in the desert when a material component is needed.
The PHB says this about the component pouch:
Component Pouch. A component pouch is a small, watertight leather belt pouch that has compartments to hold all the material components and other special items you need to cast your spells, except for those components that have a specific cost (as indicated in a spell's description).
PHB 151
The pouch has all the components your spells require, and Material Components aren't consumed unless the spell says they are:
If a spell states that a material component is consumed by the spell, the caster must provide this component for each casting of the spell.
PHB 203
So, you have mistletoe once, and you have it forever -- unless your DM rules that lose it or it goes bad, etc. Then you have to buy more mistletoe or buy a new pouch. Such a thing, however, isn't in the rule.
Unearthed Arcana / Tasha's Cauldron of Everything
A recent released play test (UA), and page 57 of Tasha's Cauldron of Everything (optional rule) provides the following to the Ranger class:
Spellcasting Focus
2nd-level ranger feature (enhances Spellcasting)
You can use a druidic focus as a spellcasting focus for your ranger spells. See chapter 5, “Equipment,” of the Player’s Handbook for a list of things that count as druidic focuses.
Best Answer
You need not change anything about the default setting in order to have people "left out" of the benefits of clerical magic.
I don't think that clerical spellcasting is as easy to come by as you make it out to be. In other words: you can easily have your harsh and gritty world. In what follows I'll always lean toward the more-utopian interpretation of things, lean on the rainbows-and-unicorns end of numerical ranges, and I think you'll see there's still plenty of room for gritty/harsh living conditions. Obviously, then, if we dial back any of those happy-happy-joy-joy assumptions we can make things even harder for people.
Demographics
You've told us you want a harsh, uncaring setting. Luckily, much of our history on this planet has been conducted in that setting so we've got lots of data to go on. I'll point you toward my favorite such tool--Medieval Demographics Made Easy--which helps us imagine D&D's pseudo-medieval implied setting using the tax rolls of 13th-C France.
This gives a baseline of one "clergy" per 40 population, and one "priest" per every 25-30 clergy. For your purposes I'm going to interpret "clergy" as an unleveled acolyte, and a "priest" as a leveled cleric.1 That means that we find a leveled cleric every 1000-1200 population.2
Villages/farmlands/wilds
Villages (according to MDME) top out at about a thousand people, so let's assume we've got a 1000-person village with one L1 cleric serving as its priest. That's two first-level spell slots per day for a thousand-person village.
In the case of illnesses remember that we can only cure two people per day. I don't feel like running a full S-I-R model here,3 but we don't need too-extreme of infection and recovery rates to overwhelm the "bonus" recovery from spellcasting. And curing an illness requires a second-level spell slot, requiring a third-level cleric!
In the case of extreme injury, just remember we only need three people seriously injured to overwhelm our poor country cleric. I've never erected a barn or taken down a tall tree, but I can easily imagine three simultaneous injuries. If a cleric can heal two but has to wait until the next day to heal the splinted broken ankle, there's your limper.
Accidental death. Let's talk size: sticking with medieval France we get a population density in arable lands of about 100 ppl/mi\$^2\$. So this village and its lands occupy about 10 square miles, or about a 3-mile (diameter) hex. Recall that without help you may only have 21 seconds of life left once you hit 0hp. The odds are not good that this accident happened within 20 seconds of our cleric =(
Cities
Cities (again, using MDME's classifications) range around 10,000 people.4 Using the same numbers as above we see that a 10K-person city should enjoy only ten leveled clerics.
But notice that the underlying numbers don't really change all that much. Travel times may go down, and with more casters we'll have some of higher levels (and more slots). But there are just so many people...
Again being generous, let's assume one cleric of each of levels one through ten, and that they use fully half their slots on daily petitioners. That's 45 spells to cast for ten thousand people, or 93 spell-levels for hoi polloi. All you need is more than one percent of the population to "need" something on a given day and you'll overwhelm the daily petitioning system. 2% would overwhelm the entire clerical-magic capacity of the city. One disease, a fire, even just a day when one of the high-level clerics is tied up in bureaucratic argle-bargle will leave some unfulfilled.
Turning the dials
Let me briefly summarize the assumptions made, and how changing them will change things:
"Clergy" are not casters, only "priests" are. They are as abundant in D&D-verse as in medieval France. Obviously, in a world where the gods walk the earth there might be more priests. But keep in mind (a) there's also the lure of arcane casting; (b) clerics are also needed to deal with the undead hordes/curses/magically-fueled religious wars inherent in such a world; and (c) somehow the D&D-verse hasn't figured out any better agricultural technology than the moldboard, so we still need 90% of people to be involved in food production.
Farmland is really rich so the region/kingdom/world is pretty densely-populated. Drop population density down to 30 ppl/mi\$^2\$ (like 13th-C. England) and one's proximity to a cleric drops commensurately.
City-based clerics spend half their spellpower helping "commoners". This one I see as a fun dial to twist. If I know anything about bureaucracy at least one or two of them definitely aren't getting their hands dirty. Perhaps some orders are martially focused and so are embedded with a standing army and none of their clerical spells go to (directly, immediately) help common folk. Perhaps some order devotes 100% of its divine power to such works. Perhaps some order has grown world-spanningly-huge and spends much of its time maintaining its own bureaucracy. These are huge cultural differences that can really change how the world feels.
The cleric in a village is a L1 caster. But one can imagine that a village where a L15 cleric has retired would be a little green patch of paradise: he attends all childbirths, so mother and infant mortalities aren't a thing. Droughts/blights? Create food and water'll sustain people and seed crops well enough to get through. Village festivals (to the cleric's god, obviously) come with a Hero's feast.
Bringing it back to reality:
The situation you describe isn't fundamentally different from our own world. There are people with physical troubles, and there are some with the power to alleviate those troubles. Why, then, do we see people in difficult circumstances? Proximity, access, cost, &c all play their roles. The same is true in the D&D-verse.
In some places charities step in. In some places social structures embody greater sympathy/antipathy toward the problem. But spell slots are a limited resource and so will evolve into their own economy, just like anything else.
1 - This, effectively, is exactly what @timster argues for in his answer.
2 - If it seems I've queered the deal from the outset by declaring "priests" to be leveled clerics rather than "clergy" (and thus dialing back by a factor of 25 the number of available clerics), I urge you to consider the alternative: 2.5% of people are leveled clerics. Given twelve classes and assuming clerics are one-twelfth of leveled characters we see 30% of the population is leveled.
Sticking with pseudo-medievalism we've got to have ~90% of the population involved with agriculture, though. So not only could you have every non-farmer a leveled NPC, one out of every five (roughly) farmers would still be, too! That's not really the setting implied by most published material. (But it's kinda a cool one, methinks. Every time you stop for dinner you've got to listen to the barkeep's old campaign stories, then the stablehand's old campaign stories, then the lamplighter's old campaign stories....)
3 - okay, that's a lie. I really want to run an SIR model incorporating a clerical healer and I did. Assuming the cleric (a) doesn't get infected ever, (b) can get to and heal two people per day, (c) healed people now have immunity and can't re-infect, and (d) the same epidemiological parameters as the SARS outbreak in Hong Kong in 2003\$^5\$, we get a peak infected population of ~15% the total population; 150 people have this disease on the outbreak's worst day. The cleric, healing two a day, just doesn't do very much for those people; there's plenty of room for some disfiguring illness to scar people. (The cleric does have a huge effect on ramping down the "long tail" at the back end of the outbreak.)
Admittedly, the underlying SIR parameters may be badly constructed for this setting: people are less-densely packed and don't travel nearly as much. But then again, hygiene and sanitation are much worse and the population may be starting at a less-healthy baseline. In short, I'm not a medieval epidemiologist, just an amateur mathematician with a copy of MATLAB.
4 - This may seem small to us--it's the size of the suburb I grew up in, for instance--but "a typical large kingdom will only have a few cities in this population range." (MDME)
5 - Razum, Beecher, Kapuan, Junghauss. "SARS, Lay Epidemiology, and Fear." The Lancet, May 2, 2003 + analysis of these data in one of my modeling classes in grad school.