I had the vague impression that Harvard and Yale, like Army and Navy, were top national football programs for a long time. But looking up stuff on wikipedia for the "What If the Ivy Leagues stayed big-time" thread, I realized their time as national powers didn't end in the 1950s or 60s, it ended much, much sooner than that. It wasn't going non-scholarship that finished them, it wasn't even the GI Bill and the post-WW2 expansion of higher ed that buried them. It dates back to the Great Depression, when it became the norm for most people to finish high school.

HArvard has 12 MNCs, last in 1920.
Yale has 27 MNCs, last in 1927.
Penn has 7 MNCs, last in 1924
Princeton has 28, last in 1950. (1920, 22, 33, 35, 50)
Brown no MNCs. 1926 team did go 9-0-1 though.
Columbia 2 MNCs, last in 1933.
Cornell 5 MNCs, last in 1939.
Dartmouth, 1 MNC in 1925

I had this impression that before the Ivy's chose to de-emphasize athletics, they were major heavyweights, and apparently that's not really the case.