I don't understand what point you're trying to draw here. William Shakespeare was by no means anonymous in his day and age and he almost certainly had to consider the views of the aristocracy and other elite figures that might watch his plays i.e. self censor. Ben Johnson, a contemporary playwright, was imprisoned for writing "The Isle of Dogs".

I think parent is saying that by self-censoring, expression others enjoy is lost, with the example of Shakespear as an expresser whose impact would have been lost if he'd decided to be anonymous instead.