It has nothing to do with class at all. It has to do with how smart you are. If you're not smart, you won't benefit from higher education, certainly post-graduate education. You have to be smart to even get in the door. Try to explain Tsiolkovsky's rocket equation and Kepler's laws of orbital mechanics to your average Trump voter. They will end up looking at you slack-jawed, then start screeching about emotions and feelings. The rocket equation doesn't care how you feel, either you produce enough delta-V and in the correct magnitude and direction, and you get to orbit, or you do not and instead fall back to earth. it's numbers and math and physics. Racists are well-known for their lack of intelligence. America is full of stupid, scared, fucked up sheep who tune into the Kardashians or reality TV for their enlightenment. Higher education won't benefit them.

The overwhelming majority of society isn't intelligent enough for higher education. It would either be wasted on them, they would flunk out, or standards would have to be lowered so low as to make their jobs irrelevant or even harmful.