>Let's go ahead and shut out the vast majority of people seeking higher education,
By eliminating government funding of education, you eliminate the scam-schools, of which there have been thousands, that have sucked money out of people seeking a higher education, and didn't realize before they were scammed, that government approval of the school has nothing to do with the quality of service provided.
Or, if you insist of government funding, then the only schools that are allowed to receive funding, are those which can demonstrate that within 90 days of graduation, 50% of the graduates have a paying job in the field in which their degree is relevant, and within 180 days, 90% of the graduates have a paying job in the field in which their degree is relevant, and within 360 days, 100% of the graduates have a paying job in the field that their degree is in, that they would not have had, had they not had the degree.