While I don't think police are omniscient superheros stopping crime before it happens, they are often true heros in every sense of the word. They put their lives on the line in very dangerous situations to try and prevent danger to others, and cops are killed in duty very regularly to no fanfare outside the local community.
Police are a public good. Without a public police force the wealthy would happily fund their own security, and most already do. There are neighborhoods in San francisco with private security teams who simply bypass the shortcomings of SFPD. I'm not sure I follow why police inherently exist to serve only the interests of the wealthy. I agree with most everything else you said.