I think it's more about ettiquette than actual safety/wear concerns.
You are stepping on someone's lifeline. It's rude, ropes are expensive. You wouldn't stand on the hood of some stranger's car (unless you wanted a round of fisticuffs or a free ride from the Po-po).
But you'll end up stepping on your own, or your partners' ropes, plenty. I know I move around quite a bit when belaying...maybe to spot at the beginning, or get out of a fall/swing zone, then back directly under the first bolt to not get dragged around in a fall, etc.