I went to a second-tier public school that never had legacy admissions. Is it really a big deal? Or is this largely symbolic? Do you see kids in your classes who are rich and visibly a level below everyone else intellectually or emotionally? (I did meet a few students who were born rich and enrolled in my second-tier university after failing out of first-tier universities, so that might be my exposure to the practice…
Not at all. The purpose of legacy admissions is predominantly to get students who could go to plenty of universities at your tier to go to your university, based on the fact that their parents are alumni. You do end up with a minority-within-a-minority population of rich students who are only there because they share a last name with a building, but frankly those students are also valuable to the rest of the student body from a networking perspective.
I'm opposed to the change. The value in a university education is not just from "going to school". You have the prestige of the university (helped by attracting noteworthy alumni), networking opportunity (helped by having current students with connections through their parents), academic quality of the student body (having the rich kids subsidize merit-based scholarships boosts this, too).
On the whole, legacy admissions (and preferential admission of rich kids in general) benefits the student body as a whole. It's the raison d'etre of private schools, and eliminating it maybe lets in another say ~1-5% of your student body's worth of students who wouldn't have gotten in otherwise, in exchange for lowering the value of getting in for everybody.