this is not a direct answer to your question, but cheese quality varies more than tomato quality, and NYC pizza in the inexpensive tier already switched to it's

this is not a direct answer to your question, but cheese quality varies more than tomato quality, and NYC pizza in the inexpensive tier already switched to it's-not-really-cheese a few decades ago, so there is little room for saving except by withholding. Possibly customers want the very visible cheese-like product more than they want the sauce so scrimping on the cheese would turn more customers away?