Carnegie Mellon is a private university, and obviously there's already a strong public commitment to college education through subsidizing the student directly.
It's a private university founded with the intent to be a public good. It exists ostensibly to be a counterweight to the ills brought about by the concentration of wealth and power under its founders, in recognition of their outsize influence on society.
I think the question is whether the donations create more resources than what is used up by a legacy admission.
For example, imagine I donate $1B to the university, with two stipulations. First, they admit my child to the CS program. Second, they use the money to perpetually expand the size of every incoming CS class by 10 students.
In that respect, the legacy admission is a net good. Yes, for four years there's a spot that's used up by my kid, but even during those four years there are 10 additional people got into the program who wouldn't have otherwise.
I realize it's not that easy, it doesn't work like that, and the size of classes at places like Harvard are not limited by the how much money Harvard has. But it seems like there could be ways to keep some kind of legacy admission program which also create a net good.
Maybe every legacy admission should be required to fund a perpetual scholarship for one financially disadvantaged student? That's both expensive enough to be rare and beneficial enough to be hard to argue with.
The “provably” in my comment is meant to indicate that people would actually be afraid of falsely claiming donations which are really payments to increase m chances of their kids’ admission, since they could be proven guilty of tax evasion.