Studying Shakespeare to learn English is like reading Journey to the West with the intention of learning Chinese.
It's primarily literature, not mechanics. While there's certainly a heavy mechanical knowledge requirement in order to read literature in any given language, the learning goals of these classes focus more on elements of artistic composition. With that said, having students produce content themselves gives them a chance to practice their own articulation. On the flip-side, being asked to do so with the poetic undertones present in most North American English classrooms might also alienate some of the students. They're not likely to give it their all if they feel it's something they aren't interested in. I think that there's merit with traditional English classes, but I feel that "English" is a misnomer. "English Literature" is a much more accurate representation of what those classes tend to be about.
To be fair, it's pretty darned hard to get kids (or anybody for that matter) excited about grammar.
English
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In England, we have English Literature.