Canticle for Leibowitz wasn't on my class reading list. We were assigned a different dystopian/post-apocalypse novel. To this day I haven't read that book, though I have a copy in my personal library.
And as mentioned, Shakespeare was meant to be seen, not read. If the class doesn't have access to any local stage productions, there are some decent movies that were made over the years of some of them.
The curriculum in my high school (part of the larger provincial public school curriculum) would have required the teachers to teach one Shakespeare play each year (teacher's choice from a shortlist), and one or more novels (again, from a list). I don't know why the Grade 12 English classes had to read such depressing stuff - between English and Social Studies that year, it was all to do with death, World War I, World War III, and post-WWIII (yes, I got the numerals right). We didn't cover WWII in Grade 12, or at least my class didn't.