We're mainly dealing with multiplayer shooters here, amirite?
A buncha people mentioned Far Cry 2(and Riddick, which I haven't played), wherein your health will regenerate up to a certain notch, but you gotta stop and use a healy if you want the whole thing back. That seems like a pretty good standard, but why have a standard?
Thing is, couldn't the devs just put multiple systems in the game, and whoever sets up the match chooses one?
"We're playing TDM on Charnel House with random-spawning Medkits-only, no regen."
"We're playing Infected Flaming Zombie Bubble Bath on Shitler's Sanctum with no life regen whatsoever, and no shotguns except the shitty one."
"We're playing Capture The Junk on Hooptie Palace with Farcry-2-Style-Regen, and up to 3 medikits per team in play at once (they respawn 10 seconds after use on a table in your team's base, but nowhere else.)"
..it wouldn't take that much extra effort, would it? Just configure each map to work with a variety of options/settings, like they already do. I haven't played Modern Warfare or any of the "big boys" of modern shootin', but Smash Brothers on Gamecube had a bajillion options you could configure before the match, and I know I've played shooters that did similar things (I think it mighta been Timesplitters or Metal Gear Online?)