For sure, the criminal justice system had gotten worse, with over-incarceration and criminalization, but I doubt that the police are your friends in the 1950s since much of the structure of police organizations hadn't changed that much.
I'm not sure if that is politically possible. The police unions start complaining when politicians start to do something (see when they turned their back on DeBlasio in front of news cameras). I'm not sure if it's fixable without repercussions on the offending officers or the union rather than the taxpayers. There is zero or near zero repercussions of the officers, the chain of command or the union for malfeasance. Of course they are going to act how they act, they're humans. The worst part is the bad officers often corrupt the good ones, or make them quit, so over time there's just the bad.
You have to put strong legal deterants against it. Personal responsibility. That is actually pretty easy to implement if legislators really wanted to.
I don't think police needs it, but crony authorities under executive control almost certainly do. Russians, Russians, Russians...