How?
By making public education a public good, paid for by the public (aka government, aka taxes) and setting real requirements to participate: grades and test scores to get in to college, can't keep up = flunk out. Community College and Trade Schools for the rest of us.
Teachers have to teach for a living. Drop "publish or perish" requirements. Researchers are not teachers. Research institutions are not schools (although they could offer internships for students to learn practical research skills while contributing to a researcher's work.)
Dorm life should be more like boot-camp living and less like a luxury vacation. A shared room, simple nutritious dining hall food, campus work-requirements, etc. This will reduce overhead costs.
Private schools can continue to charge whatever their customers will pay to be "elite". They can admit a percentage of exceptional (but $ poor) students and continue to teach the best and brightest as well as the richest in exchange for tax breaks.
Remove all government involvement in student loans. Lenders will stop loaning money for private school education without government backing. Private schools outside of the elite private universities will fade away.
Make Education Great Again. No really -make it something to be earned and valued instead of just another check-box on the job application filter.