While it was a neat idea in the first Halo (they called it a 'Shield level' and you still had a physical health level that needed health pack pick-ups) I personally think regenerative health in games makes for a dull experience. I've been playing through the first Far Cry on my PC again, and part of the experience for me is having to use an air of caution when I'm rounding an unfamiliar corner and my health is low, or the absolute JOY when I find a body armor vest. Modern shooters don't have that, in fact, a lot of modern shooters make me feel like I'm back to playing DOOM on God Mode, except I'm not 12 years old any more and I would like a big-boy challenge with my purchase, please.
Here is a great article on regenerative health by Yahtzee of The Escapist Magazine. He hit some real points that I hadn't thought of, but were rather kicking around in the back of my head in the "this doesn't feel right" section of my brain. I see regenerative health (among other things) as hand-holding, and frankly, it's hard for me to have an immersive experience as a bad-*** taking out waves of bad guys single-handed, when I apparently have the life force of a Norse God.
Maybe they'll eventually just make a game where if you leave it running for 70 years, the AI dies of old age and your immortal self wins by default... Or we could go back to fun, challenging experiences that make us think. Your choice, Ubi.