For your players' specific choices:
P1 has the right idea by picking a SAD class in the Druid, but has his dump stats off kilter. While dumping Strength, even down to 6, can be managed (especially for a Druid who should be able to travel light, as Druid defensive buffs are excellent and they are well-equipped to not need tons of rations, etal), he shouldn't put his racial +2 into it.
Given his array, I would have him dump Strength and Charisma -- Dexterity is needed for initiative, and Intelligence for skill points, so you can't dump either it turns out. Wild Shape is also more beneficial for P1 than he thinks -- Natural Spell comes at the same level as Wild Shape itself in PF, so he gets casting-while-shaped essentially "for free".
Along with that, he should put that +2 racial bonus into Wisdom and bask in the glow of a +4 starting Wisdom bonus.
P5 is also on the right track with focusing on archery -- the casting of the Ranger is not strong, and with two full Vancian casters in your party (namely, the druid and the wizard), his casting won't be needed for much, while the Dexterity-based skills will be quite useful in a rogue-less party. Furthermore, his choice of Charisma for a dump stat is a reasonable one -- it's not nearly as severe a dump as in P1's case, and many Rangers don't rely upon Handle Animal the way Druids do.
Regarding concerns about healing
Having played a Druid in a party where that was the sole access the party had to healing magic, by the way, I would strongly recommend your party obtain Wands of lesser vigor if you are willing to waive the [evil] descriptor on the spell or Boots of Earth (if Fast Healing 1 is enough) if they aren't, and give one to the druid and one to another character -- Druids can't convert to healing spells as they get Summon Nature's Ally instead, and spell slots are precious especially at lower levels.
In general:
You are right to be somewhat concerned about this...
The more relevant sum in this case is of attribute modifiers -- if it's less than 0, D&D 3.5e (and presumably PF (Pathfinder) as well as it's derived from D&D 3.5e -- if it's not a rule there, you can always port the 3.5e rule to your game as a houserule) has a rule that allows the player to reroll for their stat array.
In your case, it comes out as follows:
- P1: +3, +2, +2, +0, -2, -3 = +2
- P2: +3, +2, +2, +2, +1, -1 = +9
- P3: +3, +2, +2, +1, +1, +0 = +9
- P4: +3, +2, +2, +1, +0, -1 = +7
- P5: +3, +0, +0, +0, +0, -1 = +2
Which means that all of these arrays are acceptable, at least by the sum-of-modifiers rule; however, the +2 arrays are indeed non-trivial to work with.
However, character class and construction has much more to do with this than ability scores alone.
Character classes and builds in D&D generally depend on one or more attributes to do their job:
- For a Fighter, this is either Strength or Dexterity, but Constitution also helps
- Rogues are all about Dexterity, and can make use of Intelligence and/or Charisma
- Clerics and Druids rely highly on Wisdom as it is their casting stat, but also benefit from Strength and to a lesser degree Constitution.
- Wizards are all about Intelligence, but are helped a bit by Dexterity as well
- Sorcerers rely on Charisma and also receive a little help from Dexterity
However, not all classes are this simple, or Single Attribute Dependent (SAD). Some classes, unfortunately, are Multiple Attribute Dependent (MAD), which means they have features and functions that key off of different attributes:
- Rangers rely on Wisdom for their casting, but need Dexterity heavily for combat and benefit from Constitution and/or Strength.
- Paladins are equally troublesome, as they need Strength (or possibly Dexterity) for their melee combat while using Charisma for their casting and paladin abilities. (PF actually fixed the worst of this -- the 3.0/3.5 Paladin used Wisdom for casting, which was terribad as it meant the character had to have 3 good attribute scores at a minimum.)
Furthermore, some character classes can afford to "dump", or take a penalty in, certain stats:
- Fighters can generally dump Charisma, as they aren't expected to negotiate their way out of situations
- Wizards often dump Strength, as they aren't getting into frontline combat
- Clerics and druids will frequently dump Dexterity, especially if they aren't using ranged weapons or have Zen Archery -- that feat also allows for SAD archer Rangers, relying entirely on Wisdom.
Overall, this means that P1 and especially P5 must be more careful with how they build their characters. P5 is going to have to go with a fully SAD class with an easy dump stat, for instance -- if they're dead-set on a Paladin or two-weapon fighting (aka dual wielding) Ranger, I'd let them reroll because it's not compatible with their stats array. However, that array would make a reasonable Fighter, Cleric, or Druid.
P1 is a bit more interesting, because they have a double dump on their hands -- most classes only have one designated "dump stat". It is still possible to be effective with two stats dumped, even as severely as that array dumps them, but it takes care to avoid backing yourself into an unexpected corner by dumping the wrong stat. (Dumping Intelligence, Constitution, or even Charisma can have unexpected side effects in certain games -- it may be the case that characters with a low Intelligence will not be able to speak properly, low-hit-point/squishy characters will have trouble surviving first level, or a particularly uncharismatic character will be run out of town before the adventure can get off the ground.)
Footnote: these lists are incomplete -- I don't have experience with all the 3.x or Pathfinder core classes
Bonus: Racial bonuses shouldn't be used to "fill holes"
As to P1's racial attribute bonus? It should go to the dependent attribute for P1's build, not to fill a "hole" in their attribute scores -- you're basically always better off putting it in the strong suit, especially with a +2 bonus because that translates into an unconditional +1 to the derived modifier.
This answer includes a frame challenge.
0. Let go of the fallacy of perfect balance
What I am looking for is a good resolution, or compromise, so that my
players don't feel slighted and no one ends up with very high or very
low numbers, creating overshadowing or spotlighting issues.
Oddly enough, over the years that I played "roll 'em up" since 1975, we somehow managed to have fun without point buy. For decades. Loads of fun, with some characters a bit stronger than others. (Heck, even with point buy, please see "tiers" in 3.5 to see how "balance" can still be an issue).
Current experience: we rolled our characters in the 5e campaign I am in now. No point buy. I've known all of these guys since high school, except my nephew and the DM. That's since about mid 1970's. Differing personalities. Rolling is no obstacle to fun and success.
If all of you attend this game with "let's have fun" as the goal, then let's get to addressing your problem.
As stated, your problem isn't dice rolling or not, per the email extract you provided us. Your problem is the relationship between players and DM.
What problem should you solve first? "Player versus DM attitude."
Find Common Ground
Before session one, you need a face to face session with everybody who will play to iron out what you expect from the game, and what they expect. Listen, and then share what you expect and why you think point buy is a good idea. Then, as a full table of people, come to a consensus.
Rolling Doesn't Hurt
Rolling for stats is a 40 year old feature of RPG games that works well enough. If that is what all of your players want, where's the harm in letting them do that? Your forecasting drama and problems is not giving anyone, yourself included, the benefit of the doubt. You will all be able to have fun, regardless. Anyone griping later on gets "the look" and the following response: "you all agreed to roll for stats, let's press on with the game, make the best of the tools you have." Since you mentioned that this is the gaming group you've been with for 2.5 years, and you've been friends with some of them for about 15 years, you all already know how to have fun together. Have some faith in that already established track record.
If the opinion is divided among the players on this point, go back to point one and the pre-meeting to iron out expectations before character creation. Until you reach consensus, the game is at risk.
Play!
Once expectations are more or less aligned, play and have fun.
Have Fun!
If you aren't having fun, you are doing something wrong (as a group). That would be the topic of an entirely different question, after you all begin. I see this question as "an ounce of prevention" effort (a good idea as you know this group). Given that you've known each other a while, up to a long while, I'd be very surprised if you don't have fun if you start on the right foot. Consensus building is a means to that end that's pretty effective.
On a mechanical note, since this is 5e, an ASI (later) or a racial bonus (at start) can take the hard edge off of a low number.
Best Answer
While working on this, I realized I could can get most distribution I would like to have as a player. Which makes your method pretty close to a point-buy with a random budget. You can read further to see a comparison with 4d6.
Comparison with Point Buy
Two aspects bring this method closer to a Point Buy. First, I can choose what the shape of the array will look like. Second, I can switch dices around to get better bonus. (For example, turning a 15 to a 14 in order to raise a 7 into a 8. Raising one of the lower bonus at no cost to the higher bonuses)
The system recommended in the official rules is scaled and restricted to stats in the 8-15 range. I have never used it so I can't speak precisely about it. (I am used to non-scaled and restricted to 8-15)
Compared to the official Point Buy, your system allows for higher stats, allow for lower stats (due to lack of limits) and makes it easier to get higher numbers (due to lack of scaling). With the caveat that low stats are actually hard to get because you need low dice for them.
I can compare with the example given in the rules here and try to replicate those arrays in Anydice.
The first example array is a 3-high/3-low that makes [15-15-15-8-8-8]. By adjusting the distribution like this, I get a similar and possibly better array. The low are similar, with a 50% chance of being 8 or better, and probably a 6-7 otherwise. While one of the high are have the same probability of being a 16 or higher.
On the other hand, the average array given is [13-13-13-12-12-12] and my best approximation is closer to a mix of 13,12 and 11 (Here is the AnyDice).
So, compared to standard Point Buy, the method is worse if you try to have an average array. But better as you try to have extreme stats. On top of allowing stats above 15 which are forbidden with point-buy. I would describe it as "not balanced with point-buy, but similar in power" : the important stats are expected to be a few modifier highers and the dumpstats to be significantly lower, but not that out of the norm.
Comparison with dice-based methods
You do not give any ways that you think your players will use your method, so I'll use the way I would do it.
First I try to get my 3 main stats as high as I can. On most characters, this would be my attack stat, then Dex or Con depending on what kind of character I'm playing. Then the rest is divided as evenly to get as few glaring weakness since I do not expect to actually use those stats, I just don't want a glaring -3 on a skill or a save if I can avoid it. Lastly, my race will probably give me a bonus to my first and either my second or third highest stats.
The 20d6 method
Here is what I get with this strategy Anydice. The lines are the chances of getting at least X.
Notice how the two main stats are very likely to be at least 17 and 15 before taking into account races. With the third stat around 12-13.
Also notice how the last three stats tend to be close to one another. Similar to the standard array and 4d6 methods.
On a personnal note, I would never take an ASI over a feat with those numbers.
Comparison with 4d6
For reference, here is the probability curve for 4d6-drop-lowest and 3d6 (Taken from an article on Anydice). I will be basing the following on this curves as well as my personal experience with rolling a complete array with 4d6.
The main stat can be safely expected to be a 15-16 (+3 or better with races). With the bulk of the stats falling between 12 and 14 (+2 for important stats, +1 for most of them). And the lowest being -1 or +0.
Compared to this, your method gives:
Conclusions
I don't think this will be that gamebreaking. But I would feel like my character is a full power from Lvl1. As mentionned, I wouldn't take more than 1 ASI until my build is complete from a feat point of view.
While the 4d6 bell-curve ensures most character have a bonus around +1 in all stats and a main stat around +3 for their specialty, you method gives higher highs and lower lows. More precisely, the highs appear to be slightly better than 4d6 (by +1 usually) while the lows are significantly worse ( by probably -2).
All in all, this method appears less gamebreaking than it does at first sight. It actually looks fun for a high-power game. You will absolutely need feats to make those Lvl4-8-12 interesting. Especially for a fighter.