This is not my understanding at all.
Crime seems to have fallen during the Great Depression. Murders, which are almost always reported, fell.
Things get complicated once mass surveys replace crime reports.
Rape almost certainly increased when marital rape was outlawed. Embezzlement almost certainly decreased when cash registers were implemented.
One common way to “get rid of crime” is to gentrify, which inevitably lowers crime in a specific geographic area.
Another way to “get rid of crime” is to send criminals to prisons, where it’s extremely difficult to report crimes, and surveys of victimhood are never conducted.
I’m open to being convinced on this, but I don’t think the “mainly” cause of crime is poverty.