Yes police unions can work like that... But I feel like the police union works that way because most police are that way. The union doesn't just get that way, the way the union is needs to be supported by its members. Most game studio developers are not gonna be happy with a system that works that way.

It also has the disadvantage of being the only union that all police are part of.

I would rather point to the USPS union for an example of a union with massive problems, and given how often I read "Grieve it" on that subreddit, I'd say the union has a very different set of issues.