Actually, I think "Gotham" is key to the story, because it represents the norm to which Batman, Catwoman and The Penguin are the "other".
Burton seems to have a habit of using festivals as a method of representing an affirmation of societal norms. It is most obvious in "A Nightmare before Christmas", but you also see it in "Batman", where control of the city appears to be a contest between rival festivities: the parade that the mayor is attempting to deliver as a symbol of the city's regeneration, and The Joker's lurid maelstrom of balloons, money and poison gas. The Joker's plaintiff cry that "he's stealing my balloons!" comes from his realisation that he's lost the battle for Gotham.
In BR, Christmas is the cultural norm that is anticipated as a kind of victory over the chaotic "other". Penguin tries to subvert it in the worst fashion by destroying children, for whom Christmas exists. Batman, of course, saves Christmas, and the social fabric limps on to fight another day. But Bruce nevertheless knows he is of the "other", and that is probably contributory to the rather conflicted "Merry Christmas" he gives at the end.
In my opinion, etc.