And how do you think he (and numerous governors) cut the caseload?
They, with the permission of the Federal government, added a work requirement. When people have to work 30 hours or more a week many ended up earning more than they were on welfare and they get off welfare. And those people scamming the system by collecting two checks suddenly have to be working two jobs at once, so that sort of fraud went away as well.
It had nothing to do with changing the number of caseworkers (in fact most states *added* caseworkers). It had everything to do with changing the expectations for welfare recipients, and it worked just about everywhere it was tried, not just NYC.