Back in 2012, I went through the biographies of all the major party Presidential nominees since 1900:
From 1900 through 1984, I count 9 Harvard or Yale degrees among 44 nominees, or 0.20 per candidate (and 5 of the 9 are members of the Roosevelt family).
From 1988 through 2012, I count 15 Harvard or Yale degrees among 14 nominees, or 1.07 per candidate. That's a lot!
Since 1988, five times have major party nominees been members of Yale's Skull and Bones society, which has a monumental windowless clubhouse on the Yale campus reputed to be the final resting place of Geronimo's skull.
If we were talking about Turkey, it would seem pretty obvious that there was a weird cult around attending Harvard and Yale; and the members of the cult had been remarkably effective at conspiring to impose their Harvard-Yale-centric values upon the country at large.
And indeed, that's more or less true. For example, Harvard president James Conant worked tirelessly in the postwar era to expand Harvard's reach beyond the traditional boarding school students by using the improving psychometric testing (e.g., the SAT) to haul in the smartest young people from across the country. But because the Harvard-Yale cult has been so successful, it doesn't seem like a cultish conspiracy anymore, it just seems like the way things are and ought to be.