Adding to that, the current US fee model has the (deliberate or not) impact of turning higher education into a market - where universities essentially compete to "sell a product". Once again, ignoring the consequences of marketising education on the education system itself; as well as allowing richer people to "buy" better education; what this essentially does is inculclate the market model on young people, and society at large. That is, it creates a norm of "paying more for better education", and in doing so further weakens the principles of both solidarity, but also of having a personal stake in the welfare state, that hold up higher levels of support for a welfare state.
Are there people that still think they're paying for a "better education" when they get their kids into a famous school? I thought it was common knowledge that you can get just as good of education at State U as you can at Expensive Private U and that the biggest difference between, say, Yale and UConn is how powerful your friends will be after college.
College is already free for poor people that want to go, making it free for everybody would just make every tax payer subsidize college for the children of the rich and the middle class...and screw those bastards. They have "privilege" already, why should the rest of us have to pay to give them even more of it?
People aren't rational though, so don't underestimate the cachet of having an Ivy League education as a form of status symbol - or the old boys network it gives you access to.
In any case, it's not the offspring of millionaires suffering under the existing system. It's those from middle income backgrounds who are forced into a market dynamic and prevaling culture which leads to them apply that mindset of permanent competition to everything in life. And my little extra take is that culture and attitude of "everything" being a competition explains the more annoying side of the SJW left. Since even victimhood is about proving your credentials.