Some thoughts:

1. There's a difference between "wealth disparity" and "poverty". I can't be certain, but it doesn't seem like you're acknowledging that difference. If everyone in a given locale is "poor" (relative to some other locale, or to some previous time in history) then there is very little wealth disparity in that locale but widespread poverty. The question is whether it's the disparity that causes the crime or the poverty.

2. Crimes are ultimately committed by individuals, not demographics. An individual who commits a crime somehow had to rationalize that act. There are plenty of poor people who wouldn't even consider knocking over a 7-11 except in extreme circumstances (have to eat to live). The more interesting question for me is how an individual reaches the point where they're capable of violent crime outside of situations of dire need. In that sense, crime is as much a cultural/psychological problem as it is one of demographics. It's easy to see how someone who is very poor might start to envy those with more wealth, yet for many (most) poor people that envy (if it's even present) doesn't translate into violent crime. For some it does. Why?