I addressed this in my comment. You'd end up with schools not lowering their prices, they would just be available only to the upper class.
They most definitely do:
https://www.thecrimson.com/article/2006/10/25/tuition-increa...
In truth, the costs of these schools results from a ratchet effect. Wealthy donors buy the fancy buildings which the schools are then stuck maintaining. It’s a classic case of a white elephant [1].
In fact, when people ask why colleges are paying administrators 6-7 figure salaries while classes are taught by lecturers making a fraction of that, they say they need to compete with private industry for top talent. I would hope that an administrator making $300,000+ can come up with a more creative plan for what to do with high maintenance buildings than just "let them deteriorate".