I think this is the sentiment that is responsible for the recharging health in newer games. The problem is mostly the implementation. In the Call of Duty games, if I take cover, I'm back to full health in like 15 seconds. It's ridiculous! A better approach might be SLOW health regeneration, on the order of two or three minutes. And even then, maybe put a limit on regeneration that's proportional to the amount of damage taken. If you've just been shot in the neck, you can't really come back from that. But if someone punches you in the face every 10 minutes, it's never really going to kill you.
I always liked the locational health and damage in games like Deus Ex. Most people would probably say it's too involved for most shooters, but I don't buy that. Games like CoD (I think) and others tout their "realism" with fewer shot kills, bullet penetration etc. Of course all they went out the window when they introduced regenerating health.
Bassoon, n. A brazen instrument into which a fool blows out his brains.