Jeff, The short grass gives the player options on what club, and type of shot, to hit. Rough, greenside, boils it all down to one type of shot. Not everyone putts from low mowed collars, but, they'd be wise to consider it. Most are not wise.
Besides, the short grass is there to allow your ball to bounce and roll. It's ultimate resting place is often determined by factors outside the control of the golfer. Juxtapose to hairy grass, where the result is within a few feet of where it strikes the ground.