The leader of my citys police union is a convicted domestic abuser, was in a relationship with a student at the high school he was paid to protect, is a proud qanoner, and was fired by the city 3 times. Every time he was fired the union appealed and he kept his job. He has won multiple elections since the allegations came to light. The problem with public sector unions is that our last mayoral election was cop union sponsored candidate versus teacher union sponsored candidate. Literally both the candidates were lawyers for the unions directly before they started the campaign. If you think either group has a sweetheart contract you are shit out of luck, because the unions completely control politics here.
Unions work when the group they are bargaining with has competing interests. When the union negotiates against itself everyone else suffers.
None of those serious issues are intrinsic problems with public sector unions, though. Most of them would exist even without the union playing a role, and a well structured union could also be preventing them.
Cops not being able to be fired is 100% because of the union. Every time they negotiate a new contract and the city tries to put in the ability to fire people the police refuse to arrest anyone.
Well, we don't need to get into details, but most pro-union folks I know don't consider police unions to be workers' unions. Either way, as I said, it's not an intrinsic property of unions. It's that way because police unions exist to hold the public hostage, not because unions are bad.
Holding the public hostage is an intrinsic property of public sector unions. That's the leverage they hold. If they don't like the deal being offered they can stop working and because their roles are so important that holds the public hostage.