No, lots of things are maintained on a collective illusion. We pretend that you have to be smart to get into Yale but you could donate a building and get in. But if Yale put up a sign saying you can get in for the price of a building, now buying a building makes the admission worthless to you.

It needs plausible deniability to work.

This also completely ignores the effect on the other pupils. It's like any form of corruption, it lowers morale and makes people view their situation in a reductive and transactional manner. Ultimately it fosters an attitude which is characterised by a desire to game, control and exploit as opposed to learn, understand and engage.

I did a bit of research work at the University of Ottawa, which by necessity ends up having a sizeable contingent of diplomats' offsprings.

A guy walked up to me and straight up offered to pay me to do his senior project for him. I reported him to his academic advisor. She told me "Thanks for telling me, but there's not much we can do about it without causing an international accident." So next time we saw each other, I agreed to help him with his senior project if I got to go a few rounds with him. He didn't take me up on it.

I went to a school that had essentially this system in place. There wasn't a reverse auction, but rather, full tuition was a significant chunk of change, and as a result, a significant chunk of the student body was there on various merit-based scholarships.

You could usually tell which group a given individual was from, and saying so was a common insult. Either "Your folks may have money, but you're dumb as a post", or "You might be smart but you're poor". There were a select few students where the circles seemed to overlap...