I’m not sure about the Tammany era specifically (although I am listening to a podcast about Robert Moses which is definitely not the model to follow for getting rid of it).
On some level there’s survival of the fittest and systems that have a lot of graft become worse and worse at sustaining themselves until something breaks and a more robust system takes over.
As I said above, the fact that if I don’t like a federal law, it’s easier for me to appoint a judge that interprets it to be unconstitutional or otherwise neuter it than to pass a better law is a pretty big deal. I think it makes it so tempting to start down the road of using the courts rather than playing fair to get what you want.