Plenty of poor towns without such homicide rates and robbery. You are taking the agency out of the hands of the people committing the crimes and handing it to the circumstances.
Homicides and crime still occur, they're just not well-documented. There has to be someone collecting that data and then reporting it. That costs money, so many places just don't.
The absence of data != no activity.
Very true. Lots of police departments do their best to avoid reports, which keeps crime rates lower.