Not if we implement one of the "government pays for college" plans that are floating around progressive circles.

This is also a way to get costs under control, since the government would have enormous leverage to set a cap on the rates (the same way Medicare pays much less than traditional insurance for the same procedure). Granted you can bet that on-campus housing would become even more expensive and mandatory, but at least tuition growth might slow down.

Unfortunately the same forces that killed the Medicare for All plans are going to work against these plans. There's a ton of money to be made with the current system and the people making it are well connected politically.

A big problem with most of those plans is that they are sold as "everyone gets to go to college and the government pays for it" not that "government pays only for those who are qualified"

If they want to go to college (to have access to salaries exponentially higher than non-college graduates), and aren’t part of wealthy families, then yes they do.

At least, with the current college prices, they do.