It reminds me that Neil Gaiman & Kurt Busiek once imagined together a similar plot, a long time ago, while they were going to a convention.

The idea never became a story but Neil Gaiman recycled a part of it when he wrote "Whatever Happened to the Caped Crusader?" (in an alternate reality, the Joker was actually Alfred, an actor who impersonated the Joker because Batman needed an archenemy) and also when he wrote "A Black & White World" (in another alternate reality, both the Joker & Batman are actuallly actors and their adventures are a staged affair).