This is a red herring, and more importantly,
not actually reflected in any d20-based RPG I've ever seen. Even if we move to the less-realistic sphere of action movies and thriller novels and so on, D&D just can't cut it, and the games that base themselves tightly on D&D don't typically try to cut it.
Even if you do miss more often - you also hit more often. This is why modern weapons are designed the way that they are. That's undeniable. If it wasn't a massive advantage to be able to fire a lot of rounds very quickly, then guns wouldn't be designed that way, and we'd all be charging into battle with sabres and double-barreled shotguns or something.
Specifics, please. I've played tons of successful D&D games where flintlock weapons were involved (or more primitive weapons), or d20 games where flintlock or similar weapons were the primary weapons of the setting, and it worked. Largely because they can only be fired as fast as or more slowly than other weapons in the setting.
Where modern firearms were? No. It all just gets really silly really fast unless you completely abandon HP as anything but plot armour (as
@ardoughter suggests). I seem to recall that Spycraft 2E attempted something similar to what you're suggesting re: multiple shots/attack, but I forget the actual mechanics, and I think it translated to just not tracking ammo and having bad rolls force you to reload or something. Spycraft 1E and d20 Modern were just completely terrible for this, and got silly pretty much the first time a gun was used in combat.
I mean, I tell you what, you say you could do this, I'm not going to challenge you to put your money where your mouth is, but can you even find a game that has successfully done it? Further, can you find a game that uses the d20 or 5E rules to its advantage, and does a better job simulating action movies or TV series or the like than a game actually intended to do that?
I've played loads and loads of games where the rules were "plausible" enough. I don't have exacting standards. But D&D has a peculiar set-up which is particularly bad for this sort of thing. This is a D&D problem specifically, not an RPG problem in general.