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.