It is highly likely (IMHO) that Shakespeare "physically" wrote the actual plays, but that Bacon and Marlowe's input was intertwined throughout..
Think of them as a group of comedy writers, bouncing ideas off one another's heads in a smoky back room somewhere...
Someone noted that Will ended up with all the credit for being one of the greatest writers of his time, and if Bacon or Marlowe actually wrote the plays they "tricked" themselves out of everlasting fame..
That person didn't seem to consider the times and the consequences of expressing certain opinions if one was highly placed in the society..
Much like today, it was "un-pc" to criticize one's peers publicly... In fact, it could be injurious to one's health.. Especially if talking about the Monarchy..
A relatively un-educated commoner could get away with saying things, expressing opinions, that one of rank and privilege (and power) could not...
Perhaps Shakespeare was a man of little education, but, I don't recall that Sam Clemens had a college degree. Art can't be learned, IMHO, you are born with it; it is in-bred.
All the educated individuals in the world have not produced anything like Shakespeare, so, logically, one would assume that a lot of education is not relevant to the question.
I don't doubt at all that Marlowe had an impact on Shakespeare - how could he not? - but it must be remembered that Marlowe died in 1593, a date almost certainly before nearly all of Shakespeare's plays (and certainly his best ones) were composed.