I majored in English Literature at the university and remember that this discussion came up a couple of times, but always as a laughable matter.
AFAIK nobody really took it seriously. I have read most of Shakespeare's works and it never occurred to me that this was written by multiple writers.
The subject matter of Shakespeare's plays and poetry is very basic, human stuff: love, anger, misery, vengeance etc. I don't find it any more difficult to believe that one person wrote his plays, than to believe that Leonardo da Vinci actually painted all his paintings and invented all his inventions...
As to whether someone were subcontracted, that wouldn't strike me as too unbelievable. It's quite common with painters and sculptors, for example, to use students or partners to create works of art in their name. But they (mostly) have an active role in the creation of the artwork.
