They ultimately supervise and choose the people that hire the police, the people that set the policies for the police, and the people (both in and out of police departments) directly responsible for holding police accountable.
> Inability to fire police officers, even for gross misconduct including unlawful homocide is baked in to many jurisdictions due to PBA contracts.
I'm pretty sure there is no jurisdiction in which you can't fire a police officer convicted of unlawful homicide. It's true prosecutors aren't likely to prosecute police officers, but that's because they are elected officials that are held accountable for being sufficiently successful in prosecuting non-cops, but not for prosecuting cops.
Second, while both Constitutional law regarding due process rights attached to public civil service employment and employment contract terms may make it difficult, time consuming, and procedurally involved to fire police officers, which also makes agencies reluctant to even initiate the process, you are significantly overstating the case even absent criminal prosecution.
And third, the only reason it is possible to have contract terms that make it so hard to fire police officers for misconduct is that the the law doesn't set out accountability standards or qualifications for continuation in such roles that would make such a contract void as contrary to public policy. Which is, even if a negative choice, a legislative policy choice by elective representatives. And the decision to enter into such contracts, given that they are allowed, is also a decision made by publicly accountable officials.
So, a whole lot of different, directly publicly accountable decision makers are necessarily involved, either actively or tacitly, in permitting bad cops to continue to do bad things. If the public cared to stop it, they could through the democratic process.
They ultimately supervise and choose the people that hire the police, the people that set the policies for the police, and the people (both in and out of police departments) directly responsible for holding police accountable.