I think you missed my point.
Here is a graph of unemployment under FDR.
For most of his terms in office the unemployment rate was 10-25%. Above I said that today it is around the bottom 3% that are unemployable. That was likely true then. That means that during FDR's terms in office there were between 7 and 22% unemployed that were unemployable. I don't agree with the WPA, but it did put those people to work.
And I expect that had those bottom 3% gotten onto a WPA program, they failed at whatever they were asked to do or made life for everyone around them so miserable that their fellow workers were sick of them.