Also, William Shakespeare has no record of any formal education. His play included dialects that come from various parts of Europe, all of which Shakespeare had no record of visiting, but Edward DeVere has. So you are basically suggestion that he Shakespeare was simply a genius at birth, and knew all this without any world experience. Very unlikely.
It's not only class snobbery, it's chronological snobbery as well. Many assume that because they are not fluent in languages or particularly well traveled, the average Englishman of the 17th century could not be either.
But they were, and they were also remarkably well read by today's standards. It's probable that Shakespeare travelled on the Continent, but even if he did not, men of his day devoured traveller's tales and information from far places.
The real problem with your theory, however, is that too many of Shakespeare's contemporaries and friends left a wide paper trail establishing his authorship. If Jonson, Burbage, Marlowe, Dekker, and all the rest were involved in some complicated conspiracy to falsely attribute somebody else's works to Shakespeare, and managed to succeed to the point that nobody seriously questioned his authorship until quite recently . . . then it's the most successful conspiracy in the history of the known world. Not.
Never mind all the internal evidence and textual analysis. And if you've ever read any of the Earl of Oxford's actual work, it's plainly obvious he wasn't up to the game.
Wrong, by the way.
The King's School in Stratford provided an excellent classical education (uniform and mandated by law).