Likewise you haven't provided any motivation as to why the Civil War should be taught in history class instead of last year's American Idol winners (If you tell me prominence in popular or cultural memory, than indeed Shakespeare occupies the same place).
Shakespeare endures well because he endured for the readers, theater goers, actors, authors, poets, artists, film-makers and academics after him. Of course you could say that they are all also brainwashed by schooling and wouldn't have cared about Shakespeare (this doesn't pass the litmus test though, author's that were popular solely based on being forced in schools haven't endured c.f. Chinese or Soviet education with ideologically shaped curriculums).
No, I'm not trolling. I'm pointing out that there seems to be very little objective criteria for choosing what poetry to consume. So far it seems your argument is that it's taught because "that's the way it has been done".
The civil war is taught in the US because it had a huge impact on the development of the country. The tensions in the south today relate directly to it (confederate flags still fly today). American Idol winners are irrelevant in the context of history so equating them is silly.
Did Shakespeare's work result in the overthrowing of a government or something on that scale I'm not aware of?
Shakespeare's work has had a broad and enormous impact on art and culture through out the centuries (English and Foreign) - that you are aware of the impact of the civil war (you were taught) but not the former (Wikipedia is a reasonable starting point), is a gap in culture and education but the point stands analogously.
