First of all, it seems to make sense that crime also benefits from the same economies of scale. This could offset the improvement in policing.

Secondly, policing becomes harder in a city due to increased anonymity and the ease of hiding in plain sight. As a city grows, more and more people don't know each other. This reduces the effectiveness of social policing.

Is policing the thing that stops crime? There are obviously many parts to it including policing but a lot of things have gone wrong before the police were needed.

It's much less mysterious when you consider socioeconomic factors. In particular, they concentrate in neighborhoods which are vestiges of midcentury economies of scale (i.e. factory jobs), and are now hopeless. Urban police are pretty good at stopping violent crime from leaking into white professional neighborhoods, which is arguably city institutions' true priority.

Police tactics are only going to get you so far in communities that (justifiably) see the police as an oppressive enemy faction, where witnesses don't talk to detectives and juries don't convict.