The schools won't lose that prestige, however, because the majority of the kids they admit are academically gifted. If, say, 30% of a class are legacies, that means they pick and choose 70% of the class from academically gifted kids who are verified to be, "Our kind of people". (With all the exclusionary connotations of that phrase.)

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.