I don't think anyone is suggesting all private institutions should be tuition free. NYU chose to do it for medical school, however the progressives in USA just want public college to be tuition free.
I doubt those outcomes will come to pass. Tuition used to be basically free in the USA, and it already is in many European nations, and we didn't/don't see those outcomes that you worry about.
I did not have time, write this when I made my original post.
Just because I don't agree with free does not mean I am for the inverse which is crazy high tuitions. In my opinion the crazy high tuitions is a result of guaranteeing people loans. Demand went up on a near fixed supply thus cost went up. Then when people who probably should have not been going to school started dropping out the schools saw that as a loss of revenue and fixed the problem by lowering the bar to make sure they did not have as many dropouts thus keeping their revenue up. Nobody ever likes to see a drop in revenue even if the spike was caused by artificial means.
Free market really only works if you don't have people messing around with it. It's not a free market for schools if everybody can get a loan.
I doubt those outcomes will come to pass. Tuition used to be basically free in the USA, and it already is in many European nations, and we didn't/don't see those outcomes that you worry about.