The long ago quote about the plays of Shakespeare not being written "by Shakespeare, but by another man of the same name" gives a chuckle to Stratfordian loyalists—and to appreciators of ironic bon mots—but substitute the actual spelling of the actor William's surname—Shakspere— and the remark's amusing absurdity vanishes. "The plays of Shake-speare were not written by Shakspere" (but by a writer in need of a good pseudonym).
If the actor had actually written the plays, someone would have mentioned it when he died in Stratford in 1616—or during his lifetime. But no one did. It wasn't until the 1623 Collected Plays that the two entities (Shakspere and the Shakespeare Plays) were deliberately conflated.