It’s also why many people are upset at the idea of forgiving student loans. “I spent $20k for my degree, but Person X got into med school and is $250k in debt on their own will. Make them pay for it!”
There’s some parallels between making college/university free and the free K-12 education mandates decades ago. (Yes, it’s not “free free” but “taxed to be free”, but that’s beside the point)
Also, people don’t want their taxes raised when there’s no benefit to them. If one’s kids have all graduated, you see no reason to pay more money and get nothing in return.
Don't forget about all the big whale donors too. Universities really enjoy receiving millions of dollars for endowments, scholarships, and capital projects. So they may cater to the needs and desires of those constituents.