You can talk all you want about how "better" realism is but the fact is this: regen balances the challenge curve. The challenge curve is an important part of design. If you want to remove the regen then you need something comparably better in exchange, or a replacement for what originally handled the curve.
Personally, I hate regen because of the gameplay effects. Without regen, health is a limited resource. If I manage to ambush and get a few shots into a guy, his lower health now puts him at a disadvantage if we meet toe-to-toe again.
With regen, I can take shots at him, he'll just run away and regen. My ambush becomes a total waste of time and is unsatisfying.
Location based regen is maybe ok, if you want to do a conquest kind of thing. Time-based regen is really annoying. It forces people to avoid each other which is boring.
In single player, it forces the player char to hide and regen. This kills the flow of the game. Better to just have the health as a limited resource that the player has to manage from the start instead of a resource where losing health is punished by having to stand in the same spot for 40 seconds before moving again (e.g. Max Payne).
If you then go and slow down the player, or make them hop around on one foot, or whatever realism you layer on top of that, it will just be annoying.
Not necessarily. One of my favorite multiplayer games is Fallout Tactics, because of the cripple effect. But it has to work into the overall gameplay, and not just be there 'to be realistic'.
It fits in with the concept of medics well.. in that medics can reduce a 'crippling' penalty, but not restore health to full. It allows you to have lower bullet damage & longer firefights, by allowing every bullet to have a more interesting gameplay effect.
Let's say you have a game where limb shots are not fatal, where headshots may simply cause limited vision/concussions instead of outright killing. A shot to the arm by an AK47 might disable the arm and force the target to only use a pistol or melee weapon. A shot to the leg might make disable running, and force the target to hide or wait for backup. A close explosion might cause deafness and make the targets more vulnerable to sneak attacks.
The players are then forced to adapt to their crippled situation, and it increases the pleasure of victory if they manage to turn the tables. It will also increase the value of a healer... being down to 50% health is not so scary, but having a crippled arm and being limited to a pistol while under heavy fire is!