When I was at MIT in the sixties, all undergraduates were required to take four semesters of "Humanities," in which we read chunks of Plato, the Bible, St. Augustine, Shakespeare (King Lear, I remember) and I-forget-what-all. The current requirements actually are eight semesters properly distributed in "HASS," Humanities, Arts, and Social Sciences, and perhaps some current student will be able to say more about what that amounts to.
It wasn't a waste of time but I've never been really sure about the whole Great Books, "core" curriculum, Western canon thing. I think I learned much more about having a skeptical attitude from my science and engineering profs and from my fellow students than I did from my humanities courses. Science as taught at MIT then was not at all an authoritarian dispensation of knowledge.
The doctrine of the permanent value of certain "Great" works is sometimes called "educational perennialism," and reaches a high degree of development at St. John's College, Annapolis, where all subjects, including the sciences, are taught directly from original source texts. By all accounts it turns out well-qualified students although I'm not sure how many of them go on to engineering careers.
There is a certain arbitrary character to it. It took me a long time to figure out what the big deal about Latin and Greek was. In high school I took Latin and my understanding was that learning Latin would teach logical thought, and put me into contact with "great" works. Gradually I figured out that the reason why public high schools have Latin was that they were imitating prep schools; prep schools taught Latin because it was once an admissions requirement to Harvard; Harvard required Latin because it was imitating Oxford; Oxford required Latin because it had historic ties to the Church of England, and the Church of England was an offshoot of the Catholic-in-the-large sense church, which in turn spoke Latin (in the West) and Greek (in the East). There was also, I guess, some authentic personal enthusiasm on the part of some well-educated Brits in the 1800s for the "classics," i.e. they got a kick out of reading Horace's take on things, but I think it was mostly a cultural and historic heritage from the Church.
How many Victorian-era colleges taught Arabic so that students would be able to read al-KhwÄrizmÄ in the original, I wonder?