For the record, I’m not American nor live in the US, but I have a 19-year-old son who started attending the University of Chicago this year, studying economics. Just the tuition itself is $70k. My husband and I are lucky enough to be able to afford it - I still believe it’s an outrageous amount of money to attend college.
If you can charge for something mandatory (minimum requirement for a decent job, house, healthcare) then you can set whatever price you want for it. You just need to push it to the limit of what people can finance to keep paying for over their whole lives.
Going to a private university certainly isn’t a requirement, and in-state tuition for public universities is much, much lower (but still too high).