My daughter isn't a great reader. She's got a good vocabulary, because her dad and I do, and we've never talked down to the kids. Her drama group in high school did Midsummer Night's Dream, and she's been in love with Shakespeare ever since. She took a challenging course on Shakespeare in junior college, and enjoyed every minute of it - she now reads Shakespeare for fun. Of course, it doesn't hurt that her dad's a fan too, and has all the major films of the plays on DVD, so in addition to reading the plays, she can (and has) watched them.
Shakespeare doesn't have to be incomprehensible, but I agree that they were written to be performed, and not just read. If classes that studied the plays in high school also showed the videos, I think kids would get a great deal more out of them, and enjoy them more.