I, too, would play ANGC, but not due only to its quality, and not due at all to its exclusivity.
Instead, I would play it because, of all the world's great courses, it is the one that I could talk about with my buddies and have common ground for the discussion. They KNOW the 12th at Augusta; what % of the golfing public, meaning off this website, knows the 12th at Pine Valley, or ever will.
I'm also attracted on a deep level by the idea of walking in the steps of all of the great golfers of the past, and being able to chip from where Larry Mize chipped, or have my ball roll down the slope and almost hole out like Jack's did, or smothering a 4 iron into a pond like Seve did. Where else on the planet but ANGC could I do that?