Harvard could triple its tuition and the same people are going to apply to Harvard.

This would be true for those whose contribution would be capped based on parental earnings/assets, since their effective price would not increase. And it would be true for extremely wealthy folks whose parents can spend $1M on college and not worry about it. But for the marginal applicants who would be paying full freight under the old price but can't easily toss out another $150k/yr on tuition, there would definitely be a drop in application rates.

They might apply, but certainly won't attend if they are admitted to Stanford, Yale, etc. The higher the price differential, the more likely people would be willing to take a 'prestige' hit and go to the lower cost school.

Anyone applying from a family making 400k a year (top 2%) would still be sensitive to an 80k vs 240k/year sticker price change.

Operation Varsity Blues (https://en.wikipedia.org/wiki/Varsity_Blues_scandal) suggests there are plenty of individuals willing to pay plenty more. Some would even break the law and risk prison. If it were legal, probably many more would pay.

There are just the people who got caught!

Yeah, but the average quality of students would go down.

Plenty of people can still be fewer people

Hypothetically -- what if Stanford and Yale etc also triple their tuition at the same time?

Then some people would turn to schools 4-6.