This would just be a recipe for increasing inequality among college goers. The families who can pay for the more expensive colleges will continue to do so, while you'd be taking away the opportunities for less privileged kids to go.
I believe the question, "Why college is so expensive" is the right one, but I don't think this is the right solution.
I believe the question, "Why college is so expensive" is the right one, but I don't think this is the right solution.