You're forced to pay them, you cannot bring a competing organization, they are very hard to fire individually, they are not usually prosecuted for perjury, they get away with other stuff that would see non-cops in jail and their policies serve them and not the public at large.
This is a recipe for misfeasance, nonfeasance, and malfeasance.
You can't change outcomes just by changing uniforms. You have to change incentives. And you can't get to there via a governmental (read socialistic) system.
I would disband police departments and let folks hire what physical security or investigative services they think they need on a case-by-case basis.
People would carry arms, higher hire guards, be insured by companies that would hire investigators, and if someone needed tracking down there will be bounty hunters aplenty to do the job.
You'd get competition, lower costs, higher value, and incompetence and corruption could not last among observant customers.
I would also go to an all-torts system of retributive/restorative justice. No victim, no case.
Also no prisons or jails. The truly murderous or rape or arson inclined would find themselves being taken care of... in a far less time consuming and costly way.
