Poverty rates have actually increased since the introduction of welfare and welfare reform in the US. Long term stability of your proposal aside (see the jump in Disability dependencies that followed the welfare reform), it doesn't match the data that shows a drop in crime over the same time period.
Has it really? It dropped significantly in the 60s and 70s. Following that period, it tended to track economic trends (Poverty goes up during recession, comes back down during the good times)
