Here is the thing - these colleges only provide increased chances for low income students because they are the schools for the rich and powerful. Once the rich and powerful no longer see these colleges as the places where their kids are validated in their membership in the ruling elite, the cache of attending these schools will drop, and the benefit that attending these schools will provide to poor students will disappear.
Basically, if a Harvard degree doesn’t indicate that you are part of the ruling class, it also no longer indicates that the rare poor kid attending Harvard also should belong to the ruling class.
One the majority of the students at an elite private college are no longer from the top 20%, the top 5% will stop attending the college, and the very wealthy donors will stop donating, and those corporations which are run by the ruling elite will no longer hire graduates from these college at high rates. There will no longer be any great benefit for poor students to attend such a college. It will be something of a Pyrrhic victory.
Wanting to “bring down” the Ivy+ colleges as symbols of the wealth inequality is one thing. If those are your politic, then doing things like forcing them to accept many more lower income students makes sense.
However, wanting to flatten the income distribution of these colleges in the hope that these colleges will provide the same benefits to a large number of poor kids that it does today to rich kids indicates a alack of understanding as to the real reasons behind the power and reputations of the Ivy+ and other “elite” private colleges.
PS. The same research shows that most well known public flagships also have a highly skewed income distribution. At Wisconsin, 40% of the students come from the top 20% by income, at OSU it’s 46%, at UIUC and UMN it’s 50%, at Purdue and Berkeley it’s 54%, at U Alabama it’s 56%, at U Michigan it’s 66%, and at U Virginia it’s 67%. Those last two are as bad as any “elite” private college.