It is there in black and white
So far, no authorship theory has presented stronger evidence than the name written on the works in black and white.
By reading the plays, it is clear the author was clearly not a wealthy individual. He is also clearly from Warwickshire.
You can tell from Shakespeare’s writing that the author has a nuanced ear and understanding of the cadence and manner in which common people converse.
This literary sympathy for the masses indicates that Shakespeare was not some aristocrat or political insider, he was simply a glover’s son from Stratford. He also displays a strong familiarity with some of the grubbier aspects of Elizabethan that would likely have been outside the realm of experience of the nobility. There is a scene in the histories where Shakespeare refers to the pestilence of fleas that gather in the corner of taverns near the 'jordan' where patrons relieved themselves between drinks. Common Warwickshire vocabulary is also evident in many of his plays. In Macbeth, Banquo is described as "blood bolter'd", meaning his hair was batted with blood, echoing the sentiment that in Warwickshire, snow is said to balter on horses' feet. In a Midsummer Night's Dream, he describes a "bank where the wild thyme grows", a scene that could have been pulled straight from the banks of the River Avon.
The scenes described are by no means unique to Warwickshire. In fact, there are many parts of England that could have produced the scenes mentioned in A Midsummer Night's Dream and Macbeth. Also, just because clearly has a strong understanding of the way normal people speak and a comprehension of some of the sleazier corners of Elizabethan life does not mean he was not an aristocrat or noble. It is perfectly possible to be of relatively high social standing but still be familiar with the working classes.
[P1] Evidence in the plays suggest the author was a common man from Warwickshire. [P2] Shakespeare was a common man from Warwickshire. [P3] Therefore, Shakespeare wrote the plays.
[Rejecting P1] The scenes described are not unique to Warwickshire.