Two reasons. One was realism (ah yes, because bullet wounds go away on their own if you just sit behind cover for a couple of seconds), but the actual gameplay reason was so that you could never get stuck at any point in the game.
Take Half-Life 2 for example. Admittedly it is one of the better games, with excellent level design as far as this goes, but I once watched a cousin of mine playing and the game auto-saved at a point nowhere near any medkits (or what's the Half-Life equivalent again?). Anyway with only 15 hp left, it took him at least 10 tries of trial and error to get through the next corridor and when you just want to get to your next objective, that's not a lot of fun.