I cannot come to any other conclusion looking at the data thus far. The problem is not that new plays crowd out classics. The problem is that Shakespeare crowds out everything else.
It's easy not to see this for all sorts of reasons... a lot of Shakespeare happens in festivals, so we can pretend that doesn't count even though that's how a large number of theater goers go to their one or so play a year. TCG doesn't include productions of Shakespeare in its annual tabulations. We all love Shakespeare and it feels kinda horrible (if exciting) to think and write and say that he's done too often.
But let's face it, he is. By not looking at how much Shakespeare is done, we are leaving out a major piece of the puzzle of American Theatre.The numbers in this post are rough and have their issues, but that doesn't make them not-useful. What do you see? In the past decade, Shakespeare gets 1,163 productions, the next playwright down (August Wilson) gets 146. That's almost eight times as many productions! Yikes.
(Here is where I insert and underline a really huge caveat: The numbers are based on a really limited number of playwrights, just a brief list taken and used with a database as a thought experiment. The list is definitely not comprehensive-- for one thing, it doesn't include Mamet, Pinter or Albee or Stoppard, several contemporary playwrights who I imagine are regional staples. So when you read below percentages they are just of the playwrights on that list, when we get more complete data we'll know more, this is a gut reaction not a huge grand sweeping statement derived from large amounts of data)
As Scott Walters said in the comments, the non-Shakespearean classic plays (his definition is essentially plays written before the 20th century) make up only 25% of the total classic plays on that list of writers. It's not a comprehensive list... but that means 75% of the classical rep of this country as represented on that list is devoted exclusively to fewer than 40 works written by one playwright. Does that seem right to you? I love Shakespeare. I grew up watching his plays, I've derived great, great pleasures from reading him over the years (frequently, actually, more pleasure than seeing him.. but I don't want to get into a conversation about the quality of how Shakespeare is done because I'm not super qualified to discuss it, I don't see a lot of his plays anymore).
Maybe... just maybe, we could shift our focus just a little bit.
If you managed to move the needle on classical theater so that 50% of it was by Shakespeare and 50% of it was by other writers, what would you get? 773 bonafide pre-20th Century classics performed in this country over the last decade. That's 77 a year, or more than one per state. That's not a bad.
If you want to see more masterpieces done, perhaps the companies dedicated to doing Shakespeare with some regularity are better suited to doing them than the ones that are more used to doing new plays, and perhaps therefore that is where the pressure should be placed.
Just a thought.