That's probably true if done the way suggested, where the auctioned slots are open to anyone who pays enough money.

Suppose that instead the auction was only open to people who got put on the wait list after the regular admissions process?

Top schools get a lot more qualified applicants than they have openings for, and a lot of people end up on the wait list who are just as qualified as people who were admitted.

We just had a huge lawsuit where Harvard produced detailed evidence that they have exactly those policies, and it was never a secret before then.

https://google.com/search?q=harvard+legacy

Other private schools are no different.