The thing omitted in that observation however is that until only this very generation, being able to recall with precision what one has learned was a crucial skill in any kind of study. Moderns don't bother remembering anything (even their own phone number) because they can just "look it up". High school students unceasingly complain about having to learn the first principles of mathematics "because I can just do it with my calculator" - how much more in any other discipline (which is not so clearly procedural as mathematics) would students need a "specific education" if there is to be any hope of them learning further?
I do think that universities are mostly to blame here, having flocked to the fashion of generating money-spinning faculties (like "commerce" and "journalism") while abandoning the faculties that gave the university its identity for centuries (philosophy, history, theology).
There are some overlapping faculties (such as engineering) which both teach a mostly technical discipline while also requiring a more advanced theoretical foundation, and these probably do still belong at the university... but perhaps the time is coming when we will have to look more closely at the "BS/BA only candidates" and the "graduate studies material". Actually that's already happened, with a sharp divide between the undergrads who happily toddle off to their careers in industry and never darken the doors of the academy again, and the lifelong academics who seem never to leave at all.
Perhaps the thing I find most objectionable is the indignantly anachronistic egalitarianism on display in the comments here, for the most part by people who know nothing of education (or scholarship in general) beyond their own experiences as a one-time student. Latin and Greek are not "stupid shit" put up as a wall to keep the unwashed masses out, they were (and remain) an exceedingly useful foundation for any advanced study in any discipline with a European vocabulary. At the turn of the (last) century, French may well have taken a dominant role in European correspondence but it only worked because everyone worth writing to had a working knowledge of Latin and Greek.