Encouraging cleanliness is not the point at all. The point is: "… policing methods that target minor crimes, such as vandalism, loitering, public drinking and fare evasion, help to create an atmosphere of order and lawfulness. " Source.
In the specific case that OP is referring to with Giuliani and NYC: “Bratton directed the police to more strictly enforce laws against subway fare evasion, public drinking, public urination, and graffiti.”