I studied Shakespeare relatively extensively and while it's obviously clever, probably a big part of his appeal was his plays were vulgar. Also a lot of the things we often attribute to him inventing may have been common turns of phrase back then.

Shakespeare is Wicked or Hamilton is probably a good modern comparison.

Clearly did. It's made up. People are in awe by the complexity, meaning and poetry but in the end it's still bullshit. It's also outdated. People admire classics because of some milestone they passed but after about a decade that milestone becomes cliche.