This would save young Americans from going into crippling debt, but it would also make a university degree completely unaffordable for most. However, in the age of the Internet, that doesn’t mean they couldn’t get an education.
Consider the long term impact of this. There are a lot of different ways such a situation could go, for better and for worse.
What you describe is to some extent existing in multiple countries. Basically the degrees in industries that lack specialists get more free slots whereas the others get less. As a student you can still start studying for a fee, if you don’t match the requirements (usually it is based on grades) but you can get to a free slot later on if your grades are good enough.