Well, this is a fascinating rabbit hole. Apparently there’s some question whether Shakespeare himself was literate, since his parents and daughters seemingly weren’t.
Just keep in mind that the Shakespeare authorship conspiracy theory is the is the "the moon landing was fake" of the 1800s. The theory first gained popularly thanks to Delia Bacon in the 1850s, over 200 years after Shakespeare lived.
There's no evidence Shakespeare didn't write his plays and a lot of evidence he did (including multiple books and writings published during this life listing him as author or referring to him as an author).
Shakespeare true or not, I have often found that when one excels, others sit on the sidelines, stupefied in disbelief, then shout cries of delusion about the accolades before them.
Hence, Shakespeare cannot be real, for he excels you see...
I guess the GP is more about the idea that Shakespeare was just the first one to write all the folkloric ideas of his time in a format that people loved, instead of that unexplainable genius that created all those interesting stories. (Kinda like Disney. But we don't have the originals anymore.)
That one is a lot better accepted than the idea that he didn't write his works.
Somewhat related: "Shakespear's plays weren't written by him, but by someone alse of the same name" : an essay on intensionality and frame-based knowledge representation systems
by Douglas R. Hofstadter, Gray A. Clossman, Marsha J. Meredith.
