[RPG] How to best implement a “suppressing fire” mechanic for guns in the campaign

This house rule will almost certainly change the balance of your game -- by making it more lethal -- but whether it will "unbalance" your game is for you and your players to decide together.

Imposing save-versus-exhaustion rolls when PCs regain consciousness after dropping in combat creates a nontrivial risk of a so-called "death spiral." Once your players start losing, they'll lose faster and harder.

The first two levels of exhaustion will make combat modestly more difficult, but at the third level of exhaustion, characters suffer:

Disadvantage on attack rolls and saving throws

PHB p. 291 (emphasis mine). Once that happens, your PCs will suddenly find themselves failing spell saves they would otherwise make; taking damage they otherwise wouldn't take, and so falling unconscious more often; failing death saves they would otherwise make; and failing further saves versus exhaustion if they manage to regain consciousness before dying. Remember that death saves are already challenging, because with rare exceptions they are flat rolls with no modifiers for, e.g., high attributes or proficiency. Making death saves with disadvantage will make double-fails on rolled 1s more likely, and will make it dramatically less likely for anyone to roll that clutch 20 and spring back up with 1 hit point. (See PHB p. 197.)

And just to drive the point home, I'll note that a PC's hit point maximum is halved at four levels of exhaustion, and at six, the PC straight-up dies. No save, no second chance. Dead.

Moreover, at least with respect to published adventures, you might find that PCs will already be suffering from exhaustion from various sources at higher levels of play. I recall my own experience going from Tier 1 to Tier 2 in Adventurers' League play and discovering that I spent roughly every other session with at least one level of exhaustion. Playing a monk, a class that tends to rely heavily on ability checks (for things like Acrobatics), and constantly having disadvantage on all ability checks was a drag. (And that's to say nothing of playing a mobility-focused character who often suffered from half-speed at exhaustion level two. Ugh.) Had I to contend with saves versus exhaustion every time I dropped in combat, I expect that character wouldn't have survived.

Further balance changes to consider: your house rule makes Constitution more important than it already is. Players wanting to avoid a death spiral situation might make different character-building choices as a result, so as to prioritize Constitution more highly. Be prepared for a party full of barbarians. Likewise, anything that grants a bonus to saving throws -- such as the monk's Diamond Soul ability (PHB p. 79), the bless spell (PHB p. 219), or the stone of good luck (DMG p. 205) -- becomes more valuable.

Finally, the other part of that third level of exhaustion -- disadvantage on attack rolls -- arguably affects non-caster classes disproportionately. Disadvantage on saves will of course make it more difficult for casters to maintain concentration-based spells. (See PHB p. 203.) However, a wizard can at least sling non-concentration, save-based spells (e.g., fireball) to full effect despite exhaustion. Martial classes whose efficacy is heavily dependent on connecting with attacks will have it rough when all of their attack rolls are made with disadvantage.

All that said, the relative lethality of a game is a playstyle choice like any other. Some groups enjoy a gritty game where death lurks 'round every corner. If your group digs that kind of play, and you all will be heading into a more lethal game with your eyes open to the possibility that it'll be a short one, then there's no reason not to do so.

The short answer is “No.” The long answer is as follows:

What you’re proposing is basically making the archetype become a higher powered pseudo-caster. So let’s take a look at what the end-game modifications would create.

The monk is essentially a martial class, which means they will do fine in close quarters and, at a base level, can do fine with just Attacking. While not as hardy as say a Fighter, it certainly isn’t as spell-reliant nor squishy as say a Wizard or a Warlock. As is, the Way of the Four Elements Monk could be considered a half-caster, much like a Ranger or Paladin which can eventually gain 5th level spells. However, the upside to the Way of the Four Elements is that they can regain the resources used to cast their spell during a Short Rest and their resource is more flexible.

Your proposal turns the Monk into almost a full caster which will regain their resources on a Short Rest. So let’s make some comparisons:

Compare the Monk to a Ranger and you’ll find that with your changes, the Monk will do about as well as a Ranger when it comes to just martial fighting, but their spellcasting suddenly becomes much more potent with 6th-8th level spells meaning now they’re wildly outclassing the Ranger.

Comparing it to a Warlock, unless that Warlock has specifically built for it, the Monk should be better martially. Not only that, but the main stats utilized for the Monk’s martial and spellcasting abilities will give the added benefit of additional AC which the Warlock has no equivalent of. Finally, the Warlock is the closest in spellcasting resources to the Monk in that they regain their spell slots during a Short Rest, however this is not true of the Mystic Arcanum (6th and higher level spells) they unlock at higher levels which they can only cast once per Long Rest. So overall, I’d say that your proposal make the Four Element monk almost equivalent to a Warlock on a spellcasting basis, though i’m hesitant to really say that considering no class has the ability to cast Firestorm or Earthquake twice per short rest.

Finally compare it to the Wizard. The wizard can also regain some resources on a Short Rest, but they’re limited to spell slots of 5th or lower level. So basically we run back into the problem that the Monk is regaining their uses of these much more powerful spells than a full-on caster would.

While the Way of the Four Elements Monk is indeed written underwhelming, the way I solved this was by actually giving them passive features in addition to what they already have. While this doesn’t emulate an avatar-like character, it does at least make it more fun and viable.

If you want something a little closer to an avatar-like archetype, I supposed you could add a few 6-8th level spells with the stipulation that their cost to cast is (the level of the spell + 2) Ki and that once cast, they can’t be cast again until the monk finishes a Long Rest.

On the other hand, you could also just make a character avatar-like and role play them to fit the role. You could play something like a multiclass Monk/Druid or Monk/other spellcaster. Heck, you could even just play a straight up Druid, Sorcerer, Cleric, or Wizard and role play them as though they were a Monk of sorts.

Additional Information: A few of the passive abilities I add onto the Way of the Four Elements monk include things such as learning Cantrips from the Druid spell list at 3rd level, being able to make an Unarmed Strike as a Bonus Action whenever casting a Cantrip as an action at 6th level, or being able to make an Unarmed Strike as a Bonus Action whenever casting a spell or using an Elemental Discipline at 17th level. Basically just little things that kind of put them up alongside the Eldritch Knight archetype.

A couple others that may be iffy depending on how high-powered of a game someone wants to run includes abilities to recover Ki, such as recovering 1 Ki whenever reducing a creature to 0 hp. This is just to facilitate the use of Elemental Discipline more often, especially when throwing weaker enemies at the party.