I think regenerating health is one of those game mechanics adopted by developers in the hopes of making games more broadly accessible. In and of itself, I don't think it's either a bad thing or a good thing, it's simply a design option that's been around long enough that people take it for granted.

It's basically a tool in a dev's kit to decide just how frantic they want the action, and how frustrating they want it to be to the players. On the one hand, having a regenerating health mechanic like, say, Uncharted means that you don't have to worry about placement of healing items. One of the things Tomb Raider always got dinged for was modern-day health packs and ammo in ruins that had lain dormant and unexplored for centuries. Regenerating health mitigates one of these problems, in that it's assumed the character takes time to bandage injuries, inject some painkillers, or whatever to bring them back up to snuff.

Resistance: Fall of Man and FarCry have a different element, where your health will regenerate, but only so far. The bar you're currently on, if damaged, will regenerate itself after a few seconds, but more serious injuries that have already drained full bars of health require some form of active first aid (medkit, syringe, field surgery, etc...) to restore.

Old school games like Doom and Quake, of course, let you soldier on just as effectively at 1% health as you do at 100%, and it's only when you lose that last bit that you drop completely. At least games like Resident Evil and Dino Crisis affected the player if you got hurt, showing new animations, the player clutching a damaged area, limping, blood loss, and so forth. This is slightly more realistic, and something I'd like to see more games adopt.

The idea that a human soldier of any sort can just squat behind a wall for ten seconds then pop up good as new despite being perforated by a heavy machine gun or caught on the outskirts of an exploding frag grenade is absurd, but it's a way to keep the action going in a deathmatch, as well as reward players for taking advantage of the cover mechanic. I don't see it going anywhere, simply because it makes the game more exciting and takes one less thing (health item placement) off the developer's to-do list. :)