Not just that...he’s the most performed dramatist, the most quoted, the most well known. Even in countries that don’t teach him as often as Anglophone countries do.
But even that has its roots in how and how often he’s taught. He’s quoted (usually misquoted, or at least misapplied) because everybody has that basic familiarity. And that basic familiarity comes from him being ever present in school. And he’s performed in a large part because he’s become a resume checkbox for anybody in the dramatic arts. Anybody that wants to establish themselves as a serious actor knows that step one is do some Shakespeare, heck even retired NFL runningbacks know the path to being a respected actor runs right through your nearest Shakespeare festival (Eddie George who’s now playing Billy Flinn in the Chicago touring company, which unfortunately I didn’t have the time to see this year). It’s a self perpetuating mythology, because generation after generation is taught that Shakespeare is “serious art” then anybody that wants to make “serious art” does Shakespeare. Which makes sure there’s lots of productions, including the occasional wave of really bad movies filled with actors that really don’t have the chops.