My impression is also that many cases of police abuse in the US happen in situations where most of the police officers policing a community are not themselves members of that community, but outsiders looking down on that community.
The institutions that are most effective at "fostering a sense of community" are voluntary ones like churches and cultural centres, not coercive ones like police. Social scientists have known for a long time about the critical importance of this sort of civic and community engagement, but it is often misunderstood and considered irrelevant at a political level, especially by more liberal or radical sorts of politics which often advocate for a mixture of extreme social individualism and a radical redefinition of social groups-- generally emphasizing a simplistic view of power relations over a broader sense of community.
Additionally, they advocate mixing together people who have little in common, to obtain diversity. That's not conducive to sense of community either, as Robert Putnam's research showed[1].
[1] - https://www.puttingourdifferencestowork.com/pdf/j.1467-9477....