Health systems to me are fine the way they are, for games that need immersiveness and planning out attacks (Dead Space 2, Bioshock) and have lulls in combat and exploring (FarCry2), it works well.
For games which need run-n-gun non-stop pacing, the regen health system works well. For those kinds of games (Vanquish, Gears of War), to have to stop and think and worry about health kits/healing just takes away some of the action.
Although it seems a few more games are gravitating towards this these days, I'm not complaining. Enemies getting more brazen to come and finish you off when they know you're wounded, and responding like so is a nice touch.
I remember those games on the other end of the spectrum, 2 shots max and you're down. Bloody Rainbow Six: Raven Shield was tough as hell, I could finish almost all terrorist hunt maps. Now, after finishing R6: Vegas 2 terrorist maps all on 'Realistic', I go back and play that and can barely get past 2 levels =S