I like to think of regenerating health not as "Your character magically gets better after getting shot", but as a measurement of how close your character is to being killed. Brothers in Arms did this, by having a character caught in the open never actually get shot till he "ran out of health". Every other hit was just a representation of the enemies drawing a bead on you. I like to think other games with regenerating health are the same way.
Like Mirror's Edge, for example. Faith is able to run, jump, climb, and fight just fine after being shot because she isn't getting hit. She's just being shot at, and the health representation is how close she is to being hit, or at least hurt. Same with Call of Duty. The health could represent the same, or your body armor deflecting shots.
Games with health bars actually seem more unrealistic in the long run. At least with regenerating health, your health bar is typically much smaller. It only takes a few shots to kill you. If you survive a fight, you can logically assume you were never actually hit. With a health bar, you have a character who is actually getting shot, over and over and over again, but somehow managing to patch himself up each time he finds first aid. Unless there is some handwave like armor or something (like Halo and Half-Life), it just ends up seeming silly.
Like Mirror's Edge, for example. Faith is able to run, jump, climb, and fight just fine after being shot because she isn't getting hit. She's just being shot at, and the health representation is how close she is to being hit, or at least hurt. Same with Call of Duty. The health could represent the same, or your body armor deflecting shots.
Games with health bars actually seem more unrealistic in the long run. At least with regenerating health, your health bar is typically much smaller. It only takes a few shots to kill you. If you survive a fight, you can logically assume you were never actually hit. With a health bar, you have a character who is actually getting shot, over and over and over again, but somehow managing to patch himself up each time he finds first aid. Unless there is some handwave like armor or something (like Halo and Half-Life), it just ends up seeming silly.