Comment by apparent
The numbers look very different for a private school, which could run up to $100k for tuition, room, and board. It is almost unimaginable that attending a private college could have a positive expected value at that cost. For one thing, the incoming students will typically have stellar credentials and abilities. This means that they would not have the average outcome of a high school grad who gets no further education.
If I were faced with spending $100k/yr for my kid to go to college, I would strongly consider offering 5 tranches of $50,000 that we would together invest in business ideas over the next 5 years. Humanities and social sciences could be learned in parallel, while trying to launch businesses that bring value to the world.
The lessons learned would not be the same as those one learns in college, and the social aspects would be very different/lacking. This would clearly not work for all teenagers, but for some, it could be a much better opportunity and use of funds.
People who can afford themselves going to private schools have a reason why they prefer spending 100ks vs less. Prestige schools gets you a prestige job so "It is almost unimaginable that attending a private college could have a positive expected value at that cost" isn't necessarily true.