They also protect all of us from violent thieves, rapists, and psychopaths.
Literally no. The real psychopaths are the people who believe this bullshit copaganda.
Cops don't prevent crime. They have no legal obligation to protect us. Cops supposedly help to "punish" crime (ie. torture people in cages) but even that's bullshit. Less than 1% of rapes lead to felony convictions. And anybody who's ever been robbed can tell you that police don't do shit.