It's not exactly a jurisdictional problem. PPD absolutely can ticket for a blocked crosswalk anywhere they want (the don't have to stay off PPA's "turf". They just don't, because they can justify it by saying "the PPA covers that". But that leaves only business hour enforcement of some crosswalks and none at all on others.

For 900 or so million dollars a year the city absolutely has the right to expect more, but you're right: more finding won't fix that because those paid to give a fuck actually don't give a fuck.