When you buy food to eat-in at a pizza parlor or wherever, part of the mark-up in the price for the food you pay is for the service. Which, by the way, is why most eat-in food establishments, including those without waiters, have hired cleaning help to clear off the tables.
So while it is certainly very nice for the customer to clean up after himself, it is certainly not expected that he do so considering that he paid for the service from the restaurant.