Well now, let's see.
Let's look at Bacon, for example. (I've been interested in the "Baconian Theory" for decades.)
Sir Francis, raised by Sir Nicholas Bacon and his second wife, Lady Anne (nee Cooke), grew up to hold the same position in Queen Elizabeth 1st's court as Sir Nicholas had, that of Keeper of the Great Seal, the highest legal position in the Kingdom. (This is only one of high positions they both held under QE1)
Sir Nicholas was known as a brilliant scholar, writer, etc, and Lady Anne was well schooled - fluent in Latin and Greek = and had been tutor to the young King Edward, as well as head Lady-In-Waiting to QE1, at the time Francis was born.
Sir Francis would grow up with two learned, talented people = and become one of the world's most renowned writers himself. My theory is that he was, indeed, the natural son of Sir Nicholas, and inherited his talents as well as being benefited by his upbringing and schooling.
Theories abound that Sir Francis was the illegitimate son of QE and her lover, Rbt. Dudley, Earl of Leicester and handed over to Sir Nicholas and Lady Anne to raise as a ward.
There are too many things to explore on all sides of these theories to go into here - but I subscribe to his having been the natural 2nd son of Sir. Nicholas and Anne. Indeed, Sir Francis dedicated a publication of his Essays to Anthony, first son of Anne and 3 years older than Francis, with: "Your Entire Loving Brother".
As to using another's name as a front to one's writing in the times in which Sir Francis lived, it was a common practice. Most especially for someone of prominence and in the Queen's employ/Court, as he was. Were he, in his position, to have openly written "The Works" - with all the political rhetoric, he would've lost his head, literally.
Anyway, the theory that Wm. Shakespeare was not the author of "Shakespeare" is hardly new. It's as old as - well, as Sir Francis would be today, were he still alive.
I would heartily recommend to anyone who has a bit of a curiosity bent for history to research the subject. It's fascinating. Other contemporaries of Bacon have also been named as possibly having been the author. I lean towards Bacon.
Bottom line is: We can but theorize.
That Bacon could have been Shakespeare is thoroughly impossible. We have so much of Bacon’s writing to compare with Shakespeare’s. No writer could completely change their style, especially over that much writing.