I don't think it's possible for the stories Shakespeare told to become obsolete because he wasn't the first or last to tell them. It is my understanding that not a single one of Shakespeare's plays were original works, he retold folk tales, legends, historical events etc. (Hamlet is a Danish legend, Henry V was his attempt at a documentary...) and his versions were good enough and written down enough to become canonized as classics.

But, to a modern audience, Shakespeare's language is 400 years out of date, and not only is it obsolete language, but it's Whedonesque obsolete language. Shakespeare wrote in quippy punny poetry and the bases for a lot of his puns, a lot of the cultural references he makes, we just don't get anymore. Because of all that, I think it's a similar task as reading Chaucer in the original middle English, you can kind of muddle through but you have to keep stopping and figuring out what the hell you just read.

I'm not saying Shakespeare's plays are worthless and should be discarded, but I don't think an average teenager should be expected to read and understand it the way he might a 20th century novel. I think we owe it to students to, the way we do with Chaucer, offer the original and a more modern translation.

If it's used as a reading comprehension exercise I would recommend the script for Ten Things I Hate About You instead of The Taming Of The Shrew, for pretty much exactly this reason.