I think you're missing some significant details. The NYT did a really good episode on it last week: https://www.nytimes.com/2020/06/02/podcasts/the-daily/george...
TL;DR When a cop is fired there are several safety nets that can reinstate them. If I remember right, the union reinstates ~45% of fired officers. Neither the Chief nor the mayor have the LEGAL power to even fire bad actors in the police department. They literally cannot do anything about the problem within the law.