They're not worthless, we all just pretend "they are needed to help with the general order of society". They're like a figurehead we can all point to. You know who maintains the general order of society? Me. You. Walk down the street and look around you. Those people are the ones who determine how we all behave. In some circumstances, with a very limited local and temporary effect (cop pulls you over or tells people to get out of the street) a cop can make a change, but only because he's carrying weapons and body armor with backup on tap. Really we all are the ones in charge. What happens when we all abandon the rules we know we should follow? I think it's usually called a riot.
They do serve a purpose, but I think it's really important to realize what that purpose IS before supposing that changing the police force will drastically change the people they police or society at large.