The answer has always been to close the delta between the value of a Harvard degree and wherever else your kid can actually get into. The unspoken (or uncomfortable) aspect of that is that Harvard et al. receive outsize prestige because they're associated with outsize wealth, and access to that wealth through the personal and professional connections one can garner there.

Wealth concentration in society is the fundamental issue. When median wealth is higher and the range smaller, influential families will have less with which to "bid up" a spot at Harvard. They might choose another institution, that "wherever else" we mentioned earlier. So now your kids are friends. Or maybe not (it's not such a big deal, since they're not THAT much wealthier than you are). This becomes the dominant paradigm.

Decentralize education, as it were.