I don't recall being tasked with reading a lot of "Great Literature" in primary school and only really had some assigned to me when I got into the English gifted & talented class in high school; the non G&T classes did not. And I went to one of the better public high schools in Fairfax, VA which, at least back in the 80s, was one of the better public school districts.
"For almost 400 years in this country, and for over 2,000 in the history of the West," Moore said, "truth, knowledge, beauty and virtue were the aims of education."
With the understanding of beauty no longer a purpose of education, "art and music are dying a slow death in our schools."
The history of education in the US is rather complicated, and not easily summarized, but sufficeth to say that since the late 1800s and early 1900s the US educational system - certainly the public school system - focused on establishing minimum competencies, like basic literacy, in everyone and in providing students with the ability to prepare for the burgeoning white collar job and skilled blue collar job markets (e.g., that was/is the whole point of vocational education). The so-called "classical" education - focused on "truth, knowledge, beauty and virtue", at least in the abstract - was generally left to the private schools.
That's why the old cliche of the Three Rs - Readin', (W)riting, and 'Rithmetic - is a cliche: because the schools taught everyone how to read (at all, forget about the classics), to write (the ABCs, not a latter-day version of Plato's Republic), and to add, subtract, multiply, and divide (calculus was a long time coming to the high school curriculum and even now few kids take it).
I would also just like to point out that one of the ways liberals have managed to use the public schools to cripple the American electorate has been by de-emphasizing the Three Rs - the hard-nosed, practical aspects of education - and emphasizing the subjective and rhetorical - art, beauty, "truth" - at least inasmuch as protesting, per se, is taught as "truth" - and virtue - liberal, PC, "virtue" that is - so I would be very leery of someone who wants to continue downplaying the practical in favor of the liberal in the public schools.
Finally, I would point out that the Common Core is nothing more than a set of standards - benchmarks that students are expected to hit - and doesn't dictate the entire curriculum any teacher or school must use. So long as any given curriculum gives the students the ability to hit the benchmarks, it doesn't really matter how it does that nor does it matter if the curriculum goes above and beyond the bare minimum needed to hit those benchmarks.