You can't see your legs for the same reason you can shoot while you slide: Splash Damage wants you to be able to shoot at anytime.
So, while it may not be so accurate, you can shoot while you hop, climb, jump, and slide, and there won't be any pesky appendages blocking your vision.
Now apologize to Splamage and thank them for their amazing game.
Eh maybe later. I've been playing Bulletstorm and you can shoot and slide in that game. However, how I remember in my mind, the transition is pretty stiff. Overall, it's possible, but I'm not sure if they would be sacrificing looking low or anything like that, contradicting fluidity of the game.
I find it nice that they do have the visual cue of the hand pressing and pushing along the ground, also giving an inaccuracy cue (Not having two hands on the gun equals less accuracy). However, out of context, it looks like the guy is pulling himself along the ground.