The whole system of need-based financial aid seems to be effectively moving tuition towards perfectly elastic pricing based on how much students can pay.
Universities raise the price of tuition, then increase financial aid for the subset of students who can't pay the increase. Incremental revenue for the university still goes up as they get more revenue from anyone who can reasonably afford the increased "base tuition" amount.
There maybe a sort of monopoly here but monopolies never set their prices to free (unless they're trying to destroy competitors which is obvious not the case here)
There may indeed be grotesque stratification problems with the system but that doesn't mean some part may do the right thing occasionally. Frequently even monopolies moderate their behavior out of fear of regulation. Here perhaps schools fear the reputation hit of graduating too high a percentage of rich dimwits.
I do think it's mostly altruistic in intent, but the outcome is roughly the same as the price discrimination you'd see in a perfect monopoly.
Also, I actually think an intelligent monopoly might set their lowest price to 0 (for those who couldn't pay anything). It protects their market domination.
Also state have effectively kept their funding the same or reduced it leading to even more tuition increase costs being shouldered by the students.
As it is today, the easiest way for universities to increase funding is through tuition increase and they've been using that method more in recent decades.
Universities raise the price of tuition, then increase financial aid for the subset of students who can't pay the increase. Incremental revenue for the university still goes up as they get more revenue from anyone who can reasonably afford the increased "base tuition" amount.