It didn't start that way in NY, but now they have that option precisely because nobody can recognize them, right?
Who they are can change as long as they look and act the same. It brings down costs and allows the creator to scale.
It's better than plays because shows in different cities will have different actors and everyone knows.
But you do lose the ability to promote based on individual people. And for plays that can be a huge draw. Stars will bring people.
Think of how much bigger blueman group coull be if each had a different personality. Perhaps a cartoon could have been made.