I have not seen a single study that concluded on a national basis that there is not a correlation as well as causation link between boots on the ground policing and crime rates.

There are other variables as you suggest and using multiple regression statistical analysis one can assign relative impact to those variables on crime rates.

If you do so, you will find it is myth that income inequality leads to higher crime. It is a useful narrative for people advocating income redistribution.

It turns out when you isolate on poverty rather than wealth inequality, that poverty is the driver of crime rates. Keep in mind most crime occurs between the poor absent any presence of the wealthy.

But again, see how the narrative twists from poverty (truth) to income inequality (a falsehood).

https://soulandland.com/poverty/effects-of-poverty-on-crime/#:~:text=Poverty%20is%20the%20leading%20cause%20of%20crime%2C%20drug,found%20limited%20evidence%20that%20poverty%20directly%20causes%20crime.

If your narrative were correct, then if you forced all the wealthy people in this country to leave and take their wealth with them, you would solve income inequality problem, but likely you would increase poverty levels and crime rates. So clearly, wealth inequality was not driving crime, poverty was.

Can you fix poverty with income redistribution, so far that has never worked long term since long term it leads to reduced productivity that translates to higher poverty levels. Short term it can until the money runs out... but once it runs out, you are inevitably worse off.

I do agree that poor education, substance abuse, mental health are all contributors to poverty. And if you focus on those things, you should be able to reduce poverty at the societal level and less poverty means less crime.

But notice how the focus shifts from income redistribution to creating the means for individuals to build their own "sustainable" incomes and thereby become "vested" in society and law and order. But not every human responds to the opportunity to help themselves.

As such, the reduction in societal crime won't necessarily impact poor communities, there simply will be fewer poor communities.

But you should ask yourself if our society has spent trillions of dollars addressing the poverty and its root causes over the last 60 years, is it reasonable to assume there are short term "fixes" other than boots on the ground?