The fallacy here is the presumption that a legacy admission to Harvard or Yale has anything to do with the objective of getting a world-class education. What it does is admit you to a very exclusive finishing academy for the scions of the Ruling Class, where you will hang out and connect with other legacy admits (or occasionally invitees from similarly lofty backgrounds) . Those circles are closed to plebes who had to get scholarships or even go to classes.
Getting rid of legacy admissions won’t (as others have pointed out) keep the Ivys from having a stacked admission system. In fact, it’s already stacked by the already-discussed requirement to have expensive SAT coaching, application advisors, and candy on your personal history such as summers abroad doing facially virtuous things with others whose families can afford summers abroad looking down on poor people in “shithole countries.” Also, of course, the highly selective secondary schools with their admission-extra-points polo, yacht racing, etc. teams