I will say that during my short stint as a delivery driver for a small non-chain pizza shop, I got a flat rate (less than the delivery charge, mind you) for each delivery I took.

Not sure if that happens in all cases, but I can see the case for charging a delivery fee. Baking it in to the cost of a pizza in general would unfairly charge people eating in or picking up. With delivery, you are paying for the pizza, and then an additional service.

I still think tips should be eliminated from the equation, though.