Except, in all those examples, the other characters were just cogs. Fish has been her own machine since the pilot. And she continues to move farther and farther away from the main narrative.
The plot structure looks like this:
Batman stuff
Batman stuff
Fish
Batman stuff
Fish
Fish
Batman stuff
etc.
But that's not at all how the show works. It takes every possible opportunity to remind the viewer it's Batman.Creating Fish Mooney made sense for a lot of reasons. For one thing, it made sense that at this time, when Batman wasn't around yet and the main cop and criminal characters were still in their formative years, there would've been other adversaries.
The plot structure looks like this:
Batman stuff
Batman stuff
Fish
Batman stuff
Fish
Fish
Batman stuff
etc.