It's unlikely that voters would be ok with all-around corruption of the police, but not unlikely at all that they'd be ok with, for example, harassment or overu

It's unlikely that voters would be ok with all-around corruption of the police, but not unlikely at all that they'd be ok with, for example, harassment or overuse of force against minorities. Historically the Jim Crow south is a direct product of local policies, so I think the historical record supports this view in fact. While state and federal government aren't devoid of corruption either, at least more homogeneity can be achieved at these levels. Local jurisdictions are more prone to extreme population disparities just by virtue of being smaller.