not a whit. No confidence votes have been taken by both police and firefighters in the past. In fact IMO it makes management become more intransigent and dig in it's heels even more because of the adversarial relationship it exacerbates.
In today's world, it would seem the government wants a Politico in the office of Police Chief instead of a real cop with balls to do what really needs to be done. I can't see most east coast cities changing any time soon.
Its all political. Figure even the Sheriff of the Sheriff's Office is really the only local head of what is some county's primary LE for "patrol" voted in by voters and even that is political whether or not the candidate has a D or R next to their name.