That wouldn't be a bad idea if the United States existed in a vacuum, however it does not. The problem with the above is that the market may decide to import more educated workers to fill the void, to create more corporate headquarters in countries with a more educated workforce etc. Unfortunately, this is a subject that absolutely has to considered with international competition heavily weighed.
My daughter is going to a school in the fall. She got about 90% in school grants and scholarships. Work study is the only federal funding she got. Of course she can take out loans to do the rest. A lot of private universities don’t use tons of federal aid. Of course mileage may differ.