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.
The thing is, prestige and cost do not go hand in hand. The most expensive schools are not the most prestigious. I think Vanderbilt was the first school to hit the ignominious milestone of $100,000/yr, and they're not Ivy League, Ivy+, or perhaps even Ivy++ (if such a classification existed).