I don't think the mob should be a force in Gotham, but I'd like to see remanants of their power still polluting the city. Like, maybe Councilman Thorne is still in office even though Batman and Gordon managed to clean out most of the mafia-tied politicians, with the result being he's a scrappy, manipulative, and cunning crook who runs the remaining old school mafiosos. Maybe Penguin and his Iceberg Lounge is literally the demarcation between Thorne's skels and the Freaks of Gotham, with Penguin having a foot in both worlds.
Otherwise, I think Gotham should by and large be a chaotic, pseudo-feudalistic underworld of crime, with numerous small gangs operating with shifting loyalty, though with the Joker being the most dominant warlord (as befitting the King of Gotham thing from Suicide Squad). And some of the other Freaks shouldn't really operate organized crime gangs in the traditional sense, but instead have crews of mercenaries they gather for a handful of jobs. I don't want Two-Face bowing to Joker at all, and neither should Croc, and having them put together a small gang for specific jobs does that.
Alternatively, maybe Catwoman controls what's left of the less dangerous criminals in Gotham, like blackmail and fencing, using leftover connections from Falcone and Calabrese members.