However in the private sector this happens all the time; either forcing one company to re-organize or a re-organization happens by a company going out of business and getting replaced with another one.
Voting for a politician (especially when you are stuck with two political parties) hardly constitutes voting for a re-organization.
Maybe there is a way to create competition in some way shape or form by having several different police forces (still government sponsored) that compete for your vote or maybe something else. But there definitely is a problem that there is almost no way to properly restructure a bloated government organization when it is underperforming, and somehow that should be addressed.
The public is unhappy with Thames Water, a private company, but no amount of private sector competition pixie dust is going to make another company start digging up London's streets to provide a re-organization.
It's not a problem with governments, it's a problem with natural monopolies and that's difficult to solve. Saying "government bad" is oversimplifying.
The point is that there are some things which only government can and should do. Shutting down vital services isn't practical nor popular. People wouldn't stand for it. If a the leaders of a city the size of LA decided to shut down the police force and replace it with something different, they would be immediately voted out of office. The government isn't some external actor forcing its will on the people. The government serves the majority, a majority that prefers that not to have basic services shut down because they aren't performing optimally.