They need to let in the children of the ultra wealthy for the status symbol, money, and networking for students.
They need to let in the children of high paying donors (not always the same group as above) for the money.
They need to let in a lot of smart students to give legitimacy to the above groups and create new families of donors.
They need to have a demographic profile that roughly approximates the US demographic profile to not appear racist. They also need to have a balanced gender ratio, not overly favor a single region, etc.
They want to have a balanced class, i.e. not everyone studying computer science and economics, people who can play trombone, people for the Fencing team.
You can argue that it's basically all about giving legitimacy and prestige to the ultra donors and wealthy, but it's also about introducing high-achieving people from less privileged backgrounds to those from more privileged backgrounds in the hope that you will get new generations of wealthy donors.
I don't think this is true of any Ivy League institution (that the racial demographics mirrors that of the nation). The gender ratio and "regionality" are well-balanced, however.