Where is the documentation?
Unlike his contemporaries, there is no historical documentation to suggest Shakespeare made a living from writing plays.
Shakespeare died in 1616, before 16 of his plays had been published. They were later published in print in 1623.
As a writer for money, it seems inconceivable that Shakespeare would not want to publish and capitalise on his masterpieces while he was alive. Also, his daughter, Susanna, who automatically inherited the rights of his plays, never sought financial imbursement from the sales of the 1623 Folio. This is also not characteristic of a descendent of the author.
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.
[P1] Shakespeare wrote for money. [P2] But not all of his plays were published in his lifetime. [P3] If Shakespeare wrote those plays, he would have published them in his lifetime to maximise earnings. [P4] Therefore, Shakespeare likely did not write those plays.
[Rejecting P4] There could be any number of reasons why Shakespeare chose not to publish those plays.