Crime is based upon need, making money. People sell drugs to make money. But if everybody is cared for, they don't sell drugs and if there's no money you can't sell drugs even if you wanted to. There'd be no such thing as gambling, prostitution, or selling out, or paying off a senator or a governor. There are no senators, there are no governors so you can't pay them off. If you take away the basis or the condition that generate abhorrent behavior, you don't have abhorrent behavior.
It's hard in a monetary system to trust people.