One of the several good points in this essay on why college should be free for everyone, including the rich kids, is that affluent parents often use college to extort their children: to go to a particular school, major in a particular thing, or remain closeted if they are queer. Free college liberates kids from abusive and narcissistic parents.
I also think that a family’s wealth shouldn’t buy their kids a better education than a poor family’s kid. It’s like the old line about Coca-Cola: the rich man and the poor man got the same drink for a dime.
Thus, besides free college for all, I think we should ban all private schools.