You’re making the error in belief that criminals primarily commit crime out of necessity, rather than out of inculcated behavioral habit. At least in the US, most crimes are committed by people who were brought up from a young age in a culture of criminality. There is no ethical or moral dilemma on the part of the criminal, their behavior is fully in line with the social mores of their cultural upbringing.
The folks running in shoplifting and robbery gangs are not stealing a loaf of bread to feed their starving children, criminality is their profession.
> I do see research finding strong negative correlations between violent crime and minimum incomes
Yes, poverty and crime do correlate strongly. Although be careful about conflating violent crime and property crime with each other.
That said, correlation is not causation. There is likely /some/ causative element between poverty and crime, but it is not absolute, rather poverty is also strongly correlated with other non-criminal behaviors that both lead to poverty and lead to crime. There is definitely a cultural element in wealthy countries to generational poverty, just as there is a cultural element to criminality.
If we can break that cycle for people, it benefits society as a whole, and I think it's worth investing what we can as a society into doing so, however current research certainly doesn't support deferment of responsibility for criminality because of poverty.
The folks running in shoplifting and robbery gangs are not stealing a loaf of bread to feed their starving children, criminality is their profession.