> The student fees and tuition are mostly paid for by government backed student loans.

Which the student is required to repay, but in any case are not from the chartering government.

> There really isn't any private education in the US past high school

There are plenty of private beyond-high-school educational institutions that don't qualify for government financial aid and thus rely on purely private financing, so even if you consider “accepting government issued loans” as making an institution not-private, there is plenty of private education.

I don't see the government paying for my college... In my experience a majority of my friends have or are on track to have student debt from having to pay for college.

Technically you wouldn't see it even if it was there. For most public universities, it comes as a direct allocation from the state legislature to the university.