I’m wondering if it’s done just because it was always done, and no one got around to changing it.
It is hard to find Frum quality literature, and until recently, there was hardly even any Frum non-quality literature. Once you’re already reading secular books, there is probably nothing that is completely Kosher. Shakespeare is considered a classic and a necessity for any half-decent Literature class. Also, they probably carefully select which Shakespeare plays they read. Also, I’m not sure that I remember anything so terrible from the Shakespeare plays we read in high school, but it could be it went past me or I wasn’t paying attention.
I’m not saying it’s right; I’m just giving some of the possible reasons I can think of.