I'm an academic - have worked at a variety of institutions but never officially been at an ivy league school, so I can't strictly speaking claim ground truth. But my impressions are, sure, if your idea of the "education" part of college is to (sometimes) go to classes required for your degree and do exactly what the instructor tells you and that's it, probably it doesn't make a huge difference in terms of academics where you went to school. Everybody uses (almost) the same textbooks, after all. And academic jobs are scarce enough that two instructors of the same subject at very different institutions may actually have had similar undergraduate educations and approaches to undergraduate teaching.

What ivy league and other private research universities excel at academically is scholarly opportunities outside class assignments. If you want to reconstruct 17th century pipe organs or build robotic insects or experiment on extremophiles in Greenland or whatever, there might very well be someone who wants a student to help with something like that. Plus they probably have money to cover your expenses and pay you a stipend for it, and you don't have to compete with 500 other people for the chance. More generally, if there is a particular academic topic you as a student want to learn all about, a top university has a better chance than most places of having someone or something that can help you. But the student has to show up with the initiative and persistence to get that.

The hard part is admissions: what's the best way to find students who will of their own volition seek this kind of thing out? The simple answer would seem to be to look for kids who have a history of doing that and succeeding. But instead that produced this arms race of people seeking lots of extra academic experiences purely for the sake of getting into college and then burning out and not wanting to continue once they got there.