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.
This only works if the product isn't in demand. Degrees are in high demand - jobs require them, better jobs require multiple and higher prestige degrees. That isn't going to change.
Instead those rich enough would still get a degree, but middle and lower classes would be cut out. In the end it would create a wider gap between the classes.