“How foolish is it to think that threatening to leave is going to get the city to do anything of consequence?”
It is possible government officials will pull police from other parts of the city and swarm the area around the ice cream shop - oil on the squeaky wheel sort of thing. That could help her at the expense of others.
If that fails, she can pack up and leave with a clear conscience: “I told them I was gonna leave.”
There is a fallacy in your premise.
There are no police. There are merely salaried people in uniform