To be fair, Joe, a traditional basic pizza from Italy doesn't have cheese. That's an American addition. In southern Italy, a pizza will most likely have a thin base, with a spread of tomato sauce [not our ketchup obviously], with anchovies, olives, pseudo parmesan, that is, lightly fried bread crumbs in olive oil, seasoning, etc... and maybe some cheese as an extra..!
Of course, you can get cheese pizzas easier than anything else in places like Roma, Napoli, etc, but a real pizza doesn't necessarily have cheese. When I first visited the rellies, back in 1970, my first pizza there had no cheese. When I asked about it they looked at me aghast, as if I had sworn. Nowadays, when I make my own, I might put a little bit of mozzarella or parmesan on one, but that's about it. I don't do these pineapple-type things either.