Regenerating health isn't cheap. I think it's a very good addition to games...
I mean, it lets players take calculated risks. It allows them to be hit and feel like they're in actual danger, while not penalizing them long-term for that. It invites players to be closer to the action. It really brings that feeling of "I'm under fire!" closer. Especially in war FPS games, you want to feel like you're getting pummeled and dirtied up. Regenerating health let's that happen a lot, but without the nasty consequences of you're alays being dependent on "health pack" drops. That's another thing that regenerating help fixes: no longer are levels strewn around with health packs that seem strangely out of place... and no longer do you need a health-bar HUD, as seen in Call of Duty 3!
The point of regenerating health is to tell the player "you're in trouble." It goes You'reInTrouble You'reInTrouble You'reInTrouble and then the player has to get away. If they stay in trouble too long, THEN it kills them. If they get away, then they need to stay out of trouble awhile, and then they catch their breath, they're no longer in trouble, and they keep on playing.