I don't think that this applies to many playwrights. Shakespeare was not just playwright, but also producer. I don't think playwrights today are able to rewrite shows in the middle of a run; and they don't like it when the producer rewrites. Moreover, the producer goes to a lot more shows than the writer. Also, Shakespeare had acting experience, though that's probably not terribly rare.

My understanding is that in comparable places like Broadway, they constantly rewrite and tweak plays and musicals during the previews. Murray offers an interesting comparison:

At first glance, it may not seem reasonable to expect the United States to have 65 playwrights for every one that Elizabethan England had. But this intuitive reaction is conditioned by our knowledge that the Elizabethan playwrights included Marlowe and Shakespeare, so we tend to think in terms of 65 playwrights of their caliber. But if I were to ask the question another way—is it reasonable to expect today’s United States to have 65 times as many people who make their living from writing dramas as Elizabethan England?—the answer is of course yes. The half century from 1570–1620 had only 20 English playwrights mentioned in any of the sources, 13 of whom were significant figures.[21] Compare this with the single year of 2000 in the United States, when the Writers Guild that supplies writers for unionized television and screen projects numbered 12,735 members, about half of whom were employed during 2000.22 This figure does not count all the non-unionized people who make a living writing for television, the screen, and the stage.

TV shows certainly are constantly changing based on feedback and viewership numbers.

And is it really so rare? Looking down a list like http://www.theaterpro.com/majormodernplaywrights.htm I spot a few I recognize as working directors or actors: Beckett, Brecht, Coward, Gorky, Hellman, Ibsen (or possibly close enough to count, like Caryl Churchill's workshops)... I stop at I because I could use some breakfast but hopefully my point is made.