Parmesan cheese isn't a standard pizza topping in the US. Mozzarella cheese is what's put on pizzas.
Anyway, Parmesan cheese is pretty sharp already (i.e., strong-tasting), which is why so little of it is used, like on top of spaghetti or in a Caesar's salad. I mean, I've never seen anything marked as "sharp" to indicate its any sharper than normal. By the way, that stuff in the green shakers, that's not real Parmesan cheese.