Sorry, but I'm with
@Andy in Germany on this one.
You could use the same argument about Dickens, whose works were a scathing commentary on the societal injustices of his day. Or Huxley, who used science fiction for broadly similar ends, likewise Orwell.
It's not just about learning the texts, but also understanding the context in which they were written. of course Richard III and the various Henry plays are Tudor propaganda - you have to understand that the Tudor claim to the throne was tenuous, made even more so as it was through salic descent.
Henry VII was so paranoid about being deposed because others had a better claim than him, that England was effectively a police state during his reign, even after he had secured the succession with two sons - Arthur and Henry. And it's for the same reason that Henry VIII was so damn desperate for a male heir. Villifying Richard through satire and twisting the truth was no different to the attempts of current politicians blackening their opponents reputations, but it was effective, because at the time, large swathes of the population were still illiterate.
Plus of course, you have the fact that writers, playwrights, musicians, painters and sculptors of Shakespeare's era worked under a system of patronage, whereby they produced works, usually for their patrons and for other wealthy people, while the patron paid the bills and effectively advertised them in their particular social circles. Without such patronages, we wouldn't have the richness of literature, poetry, music, art and sculpture that we do, and the world would be all the poorer for it. But the downside of the system, is that if someone is paying your bills, you have to write / paint what pleases them. You cannot please yourself.
And the "historical" plays aside, many of Shakespeare's works are shrewd observations of the Human condition. Twelfth Night is bloody hilarious - cross-dressing, mistaken identity and drunken shenanigans, Hamlet and Macbeth highlight how ambition can drive people to do terrible things, Titus Andronicus is about horribly gruesome revenge and Merchant of Venice is about how racism twists people's perception of society.
As for the sonnets... No words speak louder to me than this:
As long as men can breathe and eyes can see,
So long lives this, and this gives life to thee.
