The fact that many of his plays were published posthumously has nothing to do with the authorship debate. Following Shakespeare's death, two of Shakespeare's former colleagues in the King's Men acting company, John Heminge and Henry Condell, collected all the plays Shakespeare wrote and published the First Folio in 1623. They did so out of an appreciation for their former colleague's work.
There could have been any number of personal or professional reasons why Shakespeare chose not to publish those plays. We cannot make wild assertions about the authorship of the plays simply because the Bard decided not to publish them in his lifetime.