That's as should be; there is no constitutional authorization for the federal government to be involved in education in any way. There are, though, other benefits to privatizing education, primarily in privatizing the financing of education. 

First: The private financing of education would eliminate all of the various Ethnic Underwater Dog-Polishing Studies classes and degree programs at a stroke. Why? Because students would be required, when seeking a student loan, to go to a private lending institution - and those institutions are going to accept or deny the applicant based on the likelihood of repayment.

Let's say a young person just finishing high school is making college plans, and will need to borrow a portion of the expenses. Let them approach a private financial institution and make their case. Student A, with a 3.9 grade point average from a charter school specializing in prepping STEM students, who intend to pursue a degree in software engineering, would be a pretty good risk. Student B, with a 2.6 grade point average from the MoonBattery Squish Academy for the Politically Correct, who intends to pursue a degree in Eastern European Queer History, would certainly be sent packing. This is as it should be; apply for a mortgage, or a car loan, or any other financing, and the lending institution is going to conduct a risk assessment; how likely is a default? Student A seems pretty promising. Student B will hopefully look good in whatever color Starbucks barista aprons are when they graduate.

Second: The private financing of education would preclude most educational institutions that don't have billion-dollar endowments from the luxury of keeping activist faculty on staff. Like it or not, every college and university would then become effectively a for-profit organization. If they fail in their core mission - producing young adults with marketable skills - then few young people will be able to obtain any financing to attend those institutions. That doesn't address the big Ivy League campuses with huge endowments, but it would make a big difference in most of the state universities around the country.

Third: Making the bar higher to attend college or university would push back on the stupid idea that every kid needs to go to college. Re-emphasize the trades! There are, always have been and always alternatives that make a compelling case to drop all the “every kid should go to college” nonsense. A good, free-market network of trade schools producing qualified welders, pipe-fitters, carpenters, and electricians would be great for young folks looking to get into the job market and in the long term, great for our economy. Our nation needs tradesmen; these are honorable jobs that can pay handsomely, and don't require sitting through semesters of general education to get started. And if a student loan is required, most of these young people would be a pretty good risk, unless one of them is an aspiring carpenter named Sanders who has just returned from his honeymoon in the Soviet Union.

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Fourth: There would still be activist students and faculty on these campuses, but they should be reduced in number and influence. The re-emphasis on equipping young skulls full of mush with marketable skills, and the tightening up of financing, should at least preclude some of the more overt nonsense. But this is a problem that will require more than just financial solutions; there will also have to be consequences for violent cases; revoking student visas and repatriating, for example, foreign students who agitate on behalf of terrorist groups, just to name one possibility.

There is a lot of work to be done to make our university system what it should be. Much of academia has lost touch with its core purpose; to teach. The current system does too much indoctrination and too little education; they consider "critical thinking" to mean "you'll think what I tell you and you'll like it." And this, like so many things troubling our country right now, won't be fixed overnight. No, messing up our institutions of higher learning was the work of generations, and fixing it will be as well. Unhitching the government from any role in financing education would be a good start, but only a start. But if we are truly going to Make America Great Again, this is something that has to be tackled.