I was hoping I'd get away with a sweeping statement. I think Harvard did have such a requirement at one point, and perhaps other early institutions, but I'm not sure when they abandoned it. I suppose I'm thinking more of the 20th century, and in particular the second half, when it simply wouldn't have been possible to take Latin at many otherwise good schools that dispatched pretty much their entire output to so-called good universities.
It is very worth remembering that Yale, Princeton Columbia, Cornell, Michigan, Brown, Williams, California (and how many others?) all required heaps of Latin at the end of the 19th and beginning of the 20th centuries. Yale dropped its Latin entrance requirement in 1931. Latin was standard cultural equipment for learning, esp. "higher learning."
See Edwin Cornelius Broome, A historical and critical discussion of college admission requirements (U. of Michigan, 1903), 66.
Studying Latin helps in a special way to overcome a self-destructive presentism and self-dissolving ahistoricity. Why special? It connects us with a vast range of history more than other likely languages. English and Spanish, for example, reach back only so far. Latin goes farther, and more importantly, it gives us more direct understanding of much material of high cultural import.