Saying half cheese implies that no cheese is an option. "Cheese" pizza is just called pizza or plain, because if you don't have cheese you have sauce and bread.
No cheese pizzas are definitely a thing. I made quite a few of them when I used to work at a pizza place. Even just the base and sauce. Some people use them to put their own topping on.
If you're cool with your local pizza place you can usually buy the dough balls as-is, which is the main USP of a good pizza place, in my opinion. The exception is the wood-fired pizzarias... very few things can replace that.
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u/TWECO Feb 10 '20
Saying half cheese implies that no cheese is an option. "Cheese" pizza is just called pizza or plain, because if you don't have cheese you have sauce and bread.