and having public sector unions is likewise bad for everyone
Unions work when the group they are bargaining with has competing interests. When the union negotiates against itself everyone else suffers.
The difference with police unions is that they work in the inverse - we're in danger when they do work. Police hold us hostage by doing their jobs (badly) and offer mob-like protection.
I'll also just that I see the police union as a perfect example of what I called a US mafia style union. In Nordic countries you can't behave like this and get away with it in a union and there are pretty strict rules for what is and what isn't a legal strike.