GreatScottMarty, all of John Paul Jones' efforts were nothing compared to the shock the British received in 1779 from a combined Spanish-French fleet led by Admiral d'Orvilliers with Don Luis de Cordova as his second. Not only was an army of 40,000 threatening to invade but the allied fleet was superior to available RN forces while the RN's forces were out of position.
Making sure THAT never happened again, plus breaking the desultory siege of Gibralter were far more important than anything John Paul Jones did. Since a genuine risk of invasion and naval disaster didn't bring down North in 1779, a hypothetical raid on Edinburgh certainly isn't.
Further, since a majority of the OTL US frigates were seized by the British or burned by the US to prevent such seizure, unless you can explain how the US can build these ships without the British noticing and taking action, which doesn't even take in to account crews, arms and equipment and supplies, British vessels waiting outside to meet ships which have literally never left port...
You also fail to explain how the Continental Congress, which couldn't even be relied on to supply/pay Washington's army, suddenly could seize most of the resources private individuals put in to the privateers. It couldn't find the financial resources to attempt what you suggest without cutting or gutting other vital interests. Certainly there was little fat to cut from Washington's army! And let Washington hear about resources being wasted after the way the first 13 frigates plus purchases failed while his army is on the verge of coming apart and he will have something to say.
As for this assumption that the US could reliably find the funds needed, given the fact that for much of the war the US was on the edge of bankruptcy and would have failed without the French...
Incidentally the CN did acquire an assortment of ships including frigates from foreign sources, primarily the French, and there's no evidence that any of the 65 ships to serve in the CN, only 11 of which survived the war, made any great difference.