Okay, so Shakespeare couldn’t have written the plays because he couldn’t possibly know about court life (notwithstanding the small size of Elizabethan London, the gossip and broadsheets, and the fact that his company is known to have appeared regularly at Elizabeth’s court).
Let’s flip that argument around, and apply it to de Vere. Shakespeare’s plays were so successful on the Elizabethan stage because they were written specifically for that stage. They displays a deep knowledge of the stage-craft. How would an aristocrat at court come by that technical knowledge?
There were several “university men,” educated at Oxford and Cambridge, who tried their hand at writing plays for the Elizabethan stage. They carefully crafted them to comply with the classical conventions on how plays should be written: strict adherence to the three unities, avoiding having distressing events like a murder played out on stage, and so on. By and large, their plays flopped. The university men then wrote broadsheets and letters complaining that the ignorant masses didn’t appreciate how plays were “supposed” to be written, according to the classical authors. You would think that de Vere, or any other aristocratic, classically educated writer would run into that problem.
By contrast, the author of the plays didn’t follow the classical conventions. He wrote rip snortin’ plays that broke the rules, and were intensely popular in his day, for the particular stage that they were written for. That suggests that the author was a person trained in the Elizabethan theatre, with little or no exposure to the classical theories of drama. Like, say, an actor who learned his trade in the theater, and had a good education from a grammar school in the basics of Latin, but not much exposure to more advanced topics like classical theories of drama.