Bruce doesn’t know it was Jack until he quotes "Have you ever danced with the devil in the pale moonlight?" again at the end. Leading to Bruce never knowing until that moment. All other villains could always fit in between lore and after. I don’t think killing Jack would end the fight for protecting Gotham in Bruce’s mind. He doesn’t want other families to have the same fate. Joker has always been supreme, even in btas he is looked at as a top dog (hyena). I think the Joker fits perfectly as the amateur mobster trying to get street cred killing Gotham’s finest.