I don't often say this, but you're wrong. I didn't quote your post before this specifically, but both express the same idea. That idea is incorrect. Literature, and art in general, does develop over time. This development doesn't make what came before obsolete. It's not like your cell phone. Once the new one comes out, you can just throw the old one away. Studying old literature, old art, isn't just a study of language. It's a study in culture. If you read Shakespeare like you read Latin, then you missed the point. It's not about translation. (This is totally ignoring the fact that English is a Germanic language, and teaching Latin sentence structure, etc would teach you nothing about where English came from. We borrowed some words not the root language.) If you taught a class on literature and only focused on what you would consider to be modern (20 years? 50? You tell me.), then you would be doing a great disservice to the students in that class.
@Falrinn: I'm not saying you need to spend a semester on Shakespeare unless you are some kind of lit major, but any intro to lit course should include him. I'm also not saying that he's the stick by which all other authors should be measured. That's a bit silly since, as you say, there are many styles and most have some merit. My participation in this thread has been to answer the question posed in the thread title. This is why we study Shakespeare, and why we are correct to do so. I'm not trying to say he's any better or worse than any other author. I am trying to say he is a huge part of the history of literature, and to ignore him in a class that is an intro to literature is insane.