Look into studies that evaluate self-reported crimes or violence, etc. Not police stats. Police stats are highly unreliable for drawing these kinds of conclusions a lot of reasons before you even consider malevolence or corruption.
Nearly all crimes that are policed are crimes of poverty. Rather than focusing so thoroughly on punitive measures, it is far better for everyone to focus on the root causes.
Most policing is just policing,
The 'tactical cops' should be punted for reasons other than cost obviously, but that's not it.
This is exactly the OP's point - it's 'luxury thinking'.
Usually when police presence goes down, crime goes up. We see this in London over the last few years.
We want more, better, police in rough ares, not less.
And good jobs, obviously, parents with stability create better conditions for their kids.