Motion-capture technology is getting pretty mature now, as is character animation, ala Gollum. I imagine they still needed to do a lot of tedious tweaking right now, but I think that one day they won't. One day, they'll be able to capture expressions and body language and translate them into an animated character with great precision without any human intervention. So where am I going with this?
Well, the main problem with stage plays is that you can't have very elaborate sets, you can't have costume changes easily, and, most of all, you can't capture the pacing of editing techniques like cuts and dissolves and montage.
I think that one day, we'll be able to put actors in motion-capture suits and render them live into computer-generated versions.. Then they can be in a flaming helicopter one second and in a hospital room the next.. The actor would just quickly change to a differnet posture and expression. (Perhaps the posture could be temporarily pre-programmed to give the actor time to move around.)
We could have live-action movies, complete with editing and stunts and all that! Granted, there will still be some things that will be difficult or impossible, like maybe a slow fade from the same actor doing one thing to them doing something else, such that they have to be on the screen doing different things at the same time.... But that would really be no different from, say, a live music performance not being able to have the singer sing over their own voice...
I think plays will always have their place, since seeing someone with the naked eye will certainly still feel different from seeing them on a screen, even knowing it's live.. But I think live but animated versions of the actors will have their place. It's certainly something I expect to see in my lifetime, and I look forward to it.