Except that when the allies had control of the sea and air, there's no way the forces on either beachhead (Salerno in 1943 or Anzio in 1944) were going to "collapse" ... NGF has that effect.
Same goes for a major landing in France in 1943.
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The only Allied amphibious operation designed to hit and stay the Axis defeated after the US entered the war were the British operations in the Dodecanese, and those were a textbook example of how not to plan or execute an amphibious operation.
Best,
I don't think it can be assumed that the Allies would have air superiority for a 1943 landing in France. IIRC the Luftwaffe was still a formidable force at that point. This is an assessment I found by CalBear from a thread on the subject some years ago:
Could the Allies have invaded? Sure.
Could the Allies have succeeded? Almost certainly not.
Among other problems is that the Luftwaffe was still open for business and the Allies would have had, at best, air parity.
The American Army was still learning its trade and was, frankly, in no shape to take on the Heer in France (look at the problems it encountered in North Africa IOTL, and that was against a fraction of what the Heer could havethrown at them in France).
Allied fighter designs did not yet have the range to provide any sort of reasonable cover, and CAS tactics were not even partly vetted.
The number and types of amphibious landing craft and ships were insufficient to put a sufficiently large force over the beach, and more critally, keep them supplied.
Allies land in France in 1943 and they get their asses kicked.