Colleges are run by big business. Every college's board and dean is full of ex-CEO types. If you restrict their ability to get funding from students, they are going to take a huge sh%t on students by cutting profs in favor of TAs and having all classes be 1500+ people held in concert halls and sports arenas.
Higher ed is extremely expensive in the US primarily because state government funding for higher ed has dropped precipitously over the past 40-50 years thanks to anti-tax advocates who have slashed state government budgets in order to reduce taxes.
The secondary cause of the explosion in tuition has been competition among schools to bring in students. As tuition goes up, students become very selective consumers. When I went to college in the late 1980s early 90s, state schools were cheap and you got what you paid for. Dorms were awful, food was crappy and the facilities were minimal. But students just moved like cattle from their public HS to the big state U in their state and did not consider going out of state. As tuition got more expensive, state schools started competing for out of state students. They did this in two ways. First, they improved facilities with nice new dorms, student centers, fancy gyms, lazy rivers, and fancy new buildings. Second, they started recruiting expensive celebrity faculty and establishing very expensive research institutes to attract students interested in computer science, engineering, medicine etc. The latter actually became a bit of a necessity as private industry learned that it did not have to provide college grads any sort of career development/training if they could get colleges to offer the same sort of training disguised as a masters program tied to a research institute. My dad graduated from MIT in the early 1960s and went to work at Raytheon in a research lab that worked on radar and laser guidance systems. It was like a graduate program with the new college grads divided up into groups who worked with a senior researcher on various projects while being taught advanced research techniques and physics. Today, you would have to do a Phd to get that kind of experience and possibly do post doc work.
The answer to higher education funding is to fund it and not force all the cost on to students. States and the federal government need to fund higher education so that tuition is a nominal burden on students.