The question whether to teach or not to teach Shakespeare in school has to do with the outcomes you wish students to achieve in schools.
We teach Shakespeare for several reasons. One reason is that each industry will introduce a specific set of vocabulary, and it will often feel like a foreign language at the beginning of employment. This Old English study helps students by offering discomfort with language and then the support to work through it and build meaning. Another reason for Shakespeare is that you can just get the surface level meaning of a text and comprehend it, but he truly offers a level for the dirty minds in a classroom, the complex minds in a classroom, the fighters and the lovers. Thus, using Shakespeare helps teachers be able to differentiate their instruction. Finally, reading Shakespeare requires interpretation, analysis, evaluation, inference, and a variety of complex higher level thinking skills. This cannot be done to the same degree with an ordinary text from American literature.
I would agree with you that Shakespeare is difficult to teach, but good teachers make it palpable and an experience that builds, not destroys skills.
So, if you don't want to see students encounter great challenge in the literature classroom, if you don't want to expose them to defining literature of the Elizabethan Era or the precursor to the Renaissance Era, if you don't care to show them where the original drama came from, then please, take Shakespeare out of schools.