I agree that JG is bound to add to GDP. But there’s a problem: JG jobs tend to be relatively unproductive. If they were amazingly productive, then relevant jobs would already be being done (by the public or private sectors). The unproductiveness of JG jobs is not necessarily a big problem, since JG provides work experience and arguably other benefits. But suppose (taking the worst case scenario) a JG so called “job” consists of picking up litter in an area where the litter problem is pretty much under control, what does that job add to GDP? The answer is “not much”.
The latter “unproductiveness” phenomenon was a significant problem with the WPA, which was why it obtained the nick name “We Piddle Around”.