Upper-middle-class American children get every advantage , from high-quality school districts to safe, clean streets on which to play, says Richard V. Reeves, author of the new book "Dream Hoarders" and a senior fellow in Economic Studies and co-director of the Center on Children and Families at the Brookings Institute.

They don't also need the boost given by legacy admissions to ensure that they get coveted seats at the country's most elite colleges.

"To operate a hereditary principle in college admissions," he tells CNBC, is unfair. Especially for a country that fancies itself to be a meritocracy. To put it bluntly, he says, all the different ways upper-middle-class parents elbow competitors out of the way to get their kids into the best colleges amounts to "cheating."

"I think it's time we stopped, and maybe that means you need to stop," he says.

Reeves went to Oxford, but, he says, that "didn't help my son get into Oxford, and he didn't get in, and it would have been seen as preposterously unfair if it had. So we might have a hereditary monarchy, but, by the way, [the members of that monarchy] don't get to go to Oxford and Cambridge anymore either because they don't get good enough grades."

That kind of preference for legacy admissions in the U.K. "disappeared in the twentieth century," he says.

It is, however, still very much alive in the U.S. And that matters a great deal, because access to elite universities is one of the primary ways the upper-middle class and upper class pass on their advantages. Reeves writes in "Dream Hoarders" that, in America, "the children and grandchildren of wealthy people end up wealthy themselves, but largely by getting a better education than through direct inheritance: because of B.A.s rather than bequests."

The legacy advantage is even more sizable than you might imagine. As the Chronicle of Higher Education reported back in 2011, based on research from Harvard, "legacy applicants got a 23.3-percentage-point increase in their probability of admission. If the applicants' connection was a parent who attended the college as an undergraduate, a 'primary legacy,' the increase was 45.1-percentage points."

Overall, according to the Chronicle, "if a non-legacy applicant faced a 15 percent chance of admission, an identical applicant who was a primary legacy would have a 60 percent chance of getting in."

Plenty of experts agree with Reeves that the status quo is unfair. Jeffrey J. Selingo at The Washington Post wrote earlier this year that "the easiest way for elite universities to bridge the growing economic divide on their campuses and have their student bodies look like the rest of America is to eliminate legacy admissions."