For the best explanation of why playwrights need companies instead of producers, here's Marsha Norman on Tracy Lett's August: Osage County:
Finally, at least for this go-round, I like what this play represents: a life-long association of a writer with a group of actors and a theater. This is why Shakespeare wrote so much, he had a whole gang of actors waiting to do his work. Go down the list — the writers who wrote a lot of wonderful plays were always associated with a community of actors they could write for: Shepard, Chekhov, Brian Friel, Alan Ackbourne, David Mamet, Lanford Wilson, Caryl Churchill, Richard Foreman, Wendy Wasserstein. Playwrights who live apart from theaters and actors have a lot of trouble getting their work done. Playwrights need to be around actors, need to be a part of a theater’s life.
[...] If we wanted to do one single thing to improve the theatrical climate in America, we’d assign one playwright to every theater that has a resident acting company. People wonder why so much great work came out of Actors Theatre of Louisville in the early days. I was there, so I know it was simply that you had everything you needed: actors who wanted to work, empty stages ready for plays and an artistic director who gave everybody a chance to do whatever they wanted as soon as they could think of it. Playwriting in America has suffered a devastating blow from the development process that keeps writers separate from the rest of the company, working on the same play for years. What playwrights want is what Steppenwolf has given Mr. Letts: a way to get a new play done, see what works, and then go on to the next one.
You can read the entire essay here.
Oh, and yes, Lindbergh 2 is going swimmingly and Lindbergh 3 is on its way down the birth canal etc. etc. etc.