And he's the only presumed writer of his time for whom there is no contemporary evidence of a writing career."
Even a quick google search would show you how obviously wrong that is.
And yes, he wrote some of the most astonishing literature ever, but it wasn't 'perfect'. He made mistakes that a university educated noble probably wouldn't have, and the plays are consistent with someone who 'hadst small Latin and less Greek' (as his contemporary Ben Johnson, who came from as humble a background, stated in his 'To the memory of my beloved Shakespeare, and what he hath left us') and what's more quite a number of the mistakes he made are unerringly consistent with mistakes made in a book by Thomas Cooper which would have been available at the Stratford grammar school at the time he would been there.
The fact that a few great writers have been taken in by this is no more surprising to me than that the creator of Sherlock Holmes believed in that fairy photo.