Yes, his movements and aggressions are nothing like real people. He's very at ease grabbing a gun, shooting and killing people, free-climbing around sheer drops and recklessly leaping from ledge to ledge! He has nice humanisms, but he's far from an ordinary Joe. That would make for interesting games. How about a difficulty level in a game that changes the fitness and skill level of the player character? At 'easy' you have fit athlete or butch space marine; at 'medium' someone in okay shape but with a noticeable bulge in the tummy and with far less than perfect aim; and in 'hard' you've a balding, tubby guy who's afraid of everything, whimpers and ducks a lot of his own, shoots wildly and quickly gets out of breath. ND's water rendering technology would be great for realistic sweat patches under the arms and on the chest!
Interesting perhaps but definitely not a fun game at all.
The worst thing to do is give the player unresponsive controls for the sake of "realism", at the end of the day this is still a GAME, and responsive controls is way more important than convincing your audience that your character is an everyman, that's why despite Drake having all those animations blended together the character has to remain very responsive.
If you somehow make the character control like a fat out of shape guy who can't shoot for beans, it would frustrate the player, it's the same problem as being shot in the Getaway and losing mobility, and having to limp around slowly, it makes no gameplay sense.