Miscellaneous Musing #7

To me, one of the mysteries of World War II is precisely why the Yanks, Canadians, and Britons proper carried out Operation Overlord, the invasion of Normandy.  The customary answer is that they needed to relieve the USSR by opening a "second front"; the "D-Day" landings, however, actually established a third front, since British, Commonwealth, and de-facto Commonwealth (that is, US) forces were already fighting in Italy. (Indeed, since the Italian campaign was just a continuance of that in North Africa, whence it was transferred upon defeat of the Axis forces in Tunisia, the Eastern Front (USSR v. Axis) was not even the first front from June 1941 to the same month in 1944; British, imperial, and Commonwealth forces were already battling the Germans and Italians in Africa in 1940, at which time the Soviet Union was still allied with Germany.  It should be borne in mind also that from December 1941, the USSR's allies were busy fighting Japan as well.)  Why didn't the Western armies forego Operation Overlord and just do then what they would do over two months later, in the obscure Operation Dragoon: invade southeast France, from Italy and North Africa?  (The advantages of doing so would have included the fact that Provence, unlike Normandy, was under the Vichy regime and thus within that section of France not occupied by the Germans; it was reasonable to expect the Vichy French to either welcome the Allies as liberators or, at the very worst, to merely put up half-hearted resistance to their landings.)