Let's say, you have a short sword in the right hand, and your left hand goes freely in the wind, allowed to do whatever she wants. (things are getting nasty).
Ow crap, yet another stupid bandit that run right into your face. You run to him, hold the left mouse button while pressing the sprint key: If handled well, a "special" animation plays (not like Fallout's vats, more like crysis, in FP view, still allowing you to move) and your free hand grabs the guy's by the neck, strangling him, while you stab his stomach in a furious mood repetitively with your short sword.
I think with the ability to play the two hands independently is the perfect occasion to bring hand do hand combat to a whole new level, where you don't just punch the poor guy in the face until he pass out. I'd really love to be able to grab people in a nice barbarian-wrestling-kung-fu-ninja-cyborg pirate-jesus-raptor style.
Being able to punch people with your free hand is already an awesome feature, being able to grapple a bit would be just pure win.
Same with objects, the "grab" function always annoyed me because you couldn't see the hand actually catch the object. You just look at it and it magically lifts itself.