Like most preppers I watched NOLA at the time of Katrina with keen interest. This included how the police, the residents and the various govt. response entities behaved. I was mesmerized, shocked, and appalled. There is no doubt but that the police were more part of the problem than they were of the solution. I am not convinced that is automatically transferable everywhere else though. NOLA is as close to a 3rd world city as have in the US. Its city govt is corrupt to the core, and the police are just part of that system. Louisiana has the highest murder rate in the nation and consistently one of the highest violent crime rates. State govt.in LA is not exactly known for its high standards.
That said, I expect that big city police in other locales will behave worse post-SHTF than their small town and rural counterparts, for the same reason that people in general will behave worse in big cities, they are anonymous. It is very difficult to be anonymous in small settings, and the public knows who the police are and where they live.
Here in VT, I am not concerned with the police becoming a gang. Most folks are armed and there just aren’t enough police to make for much of a gang. We don’t even have 24 hour State Police coverage. There are a few hours in the wee hours of the night when there aren’t any State Police on duty. Only the larger towns have their own police depts. Most towns are covered by the County Sheriffs Depts. I read in the paper that my town shares one deputy with 6 other towns for patrol duty and initial response. It is the rare day that I see a deputy go through my neighborhood on patrol. The State Police will back them up, but whether it is someone from the Sheriff’s Dept or the State Police, the closest one might be half an hour away or more unless luck of the draw has someone nearby when you call. Note that VT consistently has one of the lowest murder and violent crime rates in the nation. Clearly it is due to cultural factors and not a heavy police presence.