>Maybe the plays and sonnets read like late Tudor court poetry because they are late Tudor court poetry?
I imagine you as some sort of cartoonish stereotype of a British noble, twirling your moustache as you say: "Because surely, a mere commoner could never have written such great works!"
The fact is that Shakespeare worked at the Globe Theater as a playwright when these plays were produced, and received much critical acclaim for his writing. No one disputed that during his lifetime. Furthermore, his father was an alderman, the rough equivalent of a town councilman in Stratford, so although Shakespeare was not a noble, he did come from an educated family.
Of course, hundreds of years later, people can make up all sorts of stories to explain why someone would pour hours of work into writing poetry in iambic pentameter, see them praised, give credit to a random bum, and continue to do this for decades (even from beyond the grave, apparently). There is, however, not a shred of evidence to back any of this. The fact that the writer of those plays was clearly very talented is not evidence against them being written by William Shakespeare. The fact that "to [your] ear" they sound like something de Vere wrote is not evidence of anything either.
Shakespeare conspiracies are literally Ancient Aliens level history. "There are some details we don't know about history, so therefore aliens!" is replaced with: "there are some details of Shakespeare's life we don't know, so therefore it must have been some sort of crazy conspiracy!"