I once used Fat free "Cheese-like food product substance" on a pizza.
Don't bother. No taste whatsoever. Feh! It's foul, an emmissary of hell.
My man, fat-free cheese is indeed the curdled smegma of Satan himself! It is a feculent substance, passed off on an uwitting public as the deus ex machina of culinary decline.
Here's the deal. There are certain things in life that can be eaten in a low-fat or reduced fat mode. Cheese is NOT one of them. If the platonic ideal of a food is to be a fatty, guilty sin (chicken wings, fettucine alfredo), that is the way God intended it and to reduce the fat is to emasculate it's essential goodness. It's an insult to you and the food itself.
To make a good NY pizza, I strive to find the creamiest, most flavorful cheese money can buy. Full-fat whole milk mozz for NY-style pizzas.
If you want a lower-fat pizza, try to emulate a style that is naturally low in fat: The pizza margherita. Dough made with no oil, unadulterated tomatoes, fresh basil, and a modest amount of creamy cheese.
You'll be doing yourself a favor - the skill to coax essential goodness out of small amounts of good ingredients is a challenge in itself.
Strike any thought of fat-free cheese from your mind. Go forth and sin no more!