A former partner of mine was a St. John's alum (and champion), so I heard a lot about and thought a lot about their undergraduate program.
Of course this is a wonderful list of brilliant works. I don't know if reading nothing but primary sources is the most efficient way to become a critical thinker or knowledgeable (e.g. reading Euclid might be a treat for those who know geometry, but is it the ideal way to learn geometry?), but it certainly sounds like a great way to become cultured and a great way to spend four years, given the chance.
My feeling was also that such a heavy emphasis on classical (Western!) thought and works does its students a bit of a disservice. This is a little dramatic, but I'd say a very serious view in the postmodern, post-WWII academy is that the culmination of 3000 years of Western culture, in the country that was considered by many to be at the height of Western civilization, turned out to be the Holocaust, and that so deeply fetishizing "the canon" is problematic for that reason and others. Without dismissing the greatness of anything on this list, it's unfortunate that it's not until the third or fourth years that you start to see stuff from outside the European tradition, in very limited numbers, often just as electives. There seems to be a decent selection of works reckoning with American slavery, which is good, but if I recall and AFAICT not much about European colonialism, the Holocaust, CIA-backed coups in South America, the horrors of Stalinism, rising Asian powers, the postmodern condition, any post-sexual revolution gender politics...a robust knowledge of the Greeks is all well and good, but I don't know if that's enough to be a well-rounded citizen of the world, these days.