Can't say I've ever thought about the dirt deposited on top of the rubber by the pitcher pushing off. And I'm not sure if there is dirt deposted there by every pitcher. Are you saying you've witnessed this?
I guess I don't feel that there should be dirt deposted on top of the rubber because I am of the opinion that there isn't really much of a push off that late in the delivery. I believe there is a small sideways push with the side of the foot against the front of the rubber early in the delivery to help initiate momentum. But momentum then takes over as the stride leg sweeps forward. Right before foot plant, the hips usually need to open up and that usually requires the back foot to turn over. And, at this point, I feel momentum is pulling the back foot away from the rubber while it is turning over.
So, if a pitcher is building up a good amount of momentum, then there should be no "flick" of the foot to kick up any dirt. At least, that's what I think should happen. I'll have to watch for this.