(1) It would look bad for everyone involved.
(2) The schools would lose their prestige.
Right now, if I want a good lawyer, I look to Yale, followed by Harvard/Stanford/Chicago. I have a 70% chance of getting a brilliant lawyer, and a 30% chance of getting a rich douchebag. For law firms, it doesn't actually matter too much, since reputation is mostly circular.
If I want a good engineer, I look to MIT/Stanford/Caltech. I have a 80% chance of getting a good engineer, and a 20% chance of getting a rich douchebag. That's not a guaranteed hire, but it gets you in the door. Hopefully, my interview will screen out the rich douchebags, but it doesn't always. That model is breaking down a little bit, since people are starting to notice that the typical engineering applicant from e.g. Georgia Tech, Northeastern, or similar is better than MIT/Stanford/Caltech+++.
Upside to rich douchebags: They're past the first round of all hiring processes. Between university brand and network, their kids can always find at least upper middle class jobs. In a best case, they can go on to be president! Or if they're running a company, they don't look obviously nepotistic.
+++ It's worth noting there are sample biases here. Most qualified MIT/Stanford/Caltech graduates can find jobs without going through proletarian hiring processes, so the people who do actually apply for jobs through my web site are prefiltered.
What we're talking about is the connection, during formative years, of the academically gifted to the ultra wealthy and ultra powerful. The idea that this would result in less prestige is fanciful in the extreme.
The thing that gives elite universities their reputation both their academic reputation and the elites that attend them. If they lose the academic reputation, the unis become irrelevant and might as well be a party house for rich people; no one will care except tabloids. If they lose the elites, the universities will still be prestigious universities.
So to spell it out, what I’m saying is that rich people attending elite universities are not important for elite universities. It mainly benefits rich people.
I think when people say Princeton receives a lot of federal money, they are talking about research grants, and possibly the effective subsidy that comes from the tax deductible status of donations from rich people. Each of these adds up to a lot more money than the Pell grants.
If you take away the rich people, the school won’t be able to afford to operate this way.
I believe the point was that these schools don't need to accept subsidized student loans or other forms of federal funding. That doesn't mean only admitting rich people; they have enough resources to offer student aid to bring in the academic overachievers on their own, thus maintaining their reputation without federal help.
So the only thing that would matter is whether or not the Bush-type families of the US benefit from the system that is in place. The commenter is positing that the answer is "Yes". I agree with that assessment.