Shakespeare is most effectively taught, not just by speaking it, but also with acting - they are plays after all. The poetry suggests action, and I think it really helps to understand a character or scene if you're physically submitting yourself to the emotion of the dialogue.
Yeah but teachers don't have the time to train 30 impatient and still incompetent youngsters to the art of acting in the few hours they get.
Without at least a year of practice (and even then...), the results will be atrocious, humiliating even, and the students will be even less convinced.
You should not study Shakespeare in school, it needs a lot of things to be appreciated, and hence it's a terrible material given the school constraints.
