Shakespeare is very funny and crude, but he also wielded a larger vocabulary than we're used to in our penny theatre (TV shows, popular YA books, etc.) We also know that, if nothing else, poetry is good exercising for both sides of the brain, and most people won't bother with it outside of school. (There are more reasons to teach these things but I'm setting them aside.)

We don't even try to teach what was considered scholarly in 1600, let alone in Latin and French. Those works were also considered archaic back then, too.