While textual arguments may go on, a writer for the Guardian asserts that new research findings by manuscript scholar Heather Wolfe pretty much prove that the Shakespeare who wrote the plays was indeed the Shakespeare from Stratford, and not some Earl or other.
Whenever the "controversy" is resurrected, with everybody presenting their evidence, it's routinely asserted that alas nobody has the proof and the available information has been so thoroughly analyzed that it's unlikely to be settled unless something completely new turns up.
That turns out to be nonsense as well. Because Heather Wolfe found the evidence in the library. She just looked where earlier researchers didn't--in the controversy over the Stratford Shakespeare's attempts to get a family coat of arms approved. Though she doesn't make sweeping claims, she found enough to settle the matter--contemporaries knew that the Stratford Shakespeare and the playwright were the same.
This adds to what was already a pretty convincing case made by other scholars for Shakespeare as the author of his own plays. Opponents built their doubts on the class system. They assumed that someone brought up in a provincial town couldn't get an adequate education, but the Stratford Shakespeare had available to him a classical education more rigorous than most university students can get today.
So if it wasn't education, it must be because lower middle class provincials, perhaps even raised Catholic, couldn't possibly have that level of verbal expression, let alone genius.
Maybe a strange visitor from another planet with powers far beyond those of mortal men?