The Comedian never had anything that set him apart like the Clown and the Criminal. He was just the Joker. So of course that's the only way to make him relevant to the story. Despite being the least interesting. And none of the main characters come across great here.

Just thinking aloud here, but if Batman knows who the Comedian is, then he knows when he was first active. Which means that he should be able to definitively answer the question of which Joker came first between the Comedian and the Criminal. So I don't think that the ending is at all ambiguous. If the Killing Joke origin is intact, and it is to some extent, then the Criminal does not have a role in the Comedian's creation. For this reason, I agree with PurpleGlovez take that the Comedian is the one true Joker and perhaps always has been. Though this would make the purpose for the three Jokers in the story largely superfluous to Joker's plan with Joe Chill.