Realism has jack to do with it. It's not an improvement, it's just different. They're not interchangeable. It's like saying first person view is an improvement over third person view. Or over-the should look aim is preferrable to auto-targetting. They do different things. Try throwing a regeneration mechanic into any Half-Life game, the game would become a joke. It all depends on what they're going for.
John Mclane would have probably used medkits, in honesty. Games with regenerating health typically have some kind of formal or informal safety mechanic (cover being common, whether it's press a button to flush against a wall or simply press duck behind it) to fall back on while the health regenerates. Games that use medkits are often more flexible, sometimes allowing gung-ho maneuvers (though Halo does include more allowance for this than some others with regenerating health) because they can allow you to take more damage, but you have to ration it. A regenerating health mechanic can't allow that unless they're opting for near invincibility because they drop any real rationing. What this would come down to is if they want the player to hide behind a wall while firing, moving forward then pulling back constantly, or just wade straight in and go for broke.
Though I will admit regenerating has to be easier from a development POV. Designers never have to worry about player rationing of health, how to set up encounters to allow for gung-ho approach and then give them downtime afterwards to compensate for low health, or anything of that nature.
Aside that Halo/CoD2 level regenerating health would pretty much prevent the appearance of a health based skill. Which I think would be a good customization allowance for an RPG.
Edit: That would be an interesting character trait style option. Walk-it-off: Character can recover from most damage very quickly, however has a lower threshold. Or conversely, Soak-it-up: Character can take much more damage, but recovers from damage much slower.