That, and a sane Joker would probably have to go by an official name since, without the Joker look or breed of insanity, he wouldn't have a reason for the multiple choice past and could be recognized. I doubt DC would ever go that route. We're not supposed to know who Red Hood One really is.
I am curious to see how long Joker's "death" manages to last. Snyder will probably keep it permanent up until the end of his run, considering how much he's emphasized Endgame as his "last" Joker story, and leave it up to the next writer to do with it what they will. Maybe he'll address the idea that Joker always comes back in some form, even if it's not The Joker, like in the Detective Comics #27 story, but I don't see the actual Mr. J popping up again under Snyder and Capullo.
It would be nice to see Joker stay on the bench for at least a little while, maybe not too long though, so other Bat-villains can get more of a chance at the spotlight and someone has a really good idea for bringing him back.