I think I get you now.
You are comparing invading the south of France in mid- 1943 with the OTL invasion of 1944. You believe that this would be a more effective use of resources and end the war quicker than an Italian mainland campaign.
I think I disagree because this will leave Italy (and its Navy and units in the Balkans) still in the war, eliminate Foggia heavy bomber bases, and just move the forces involved in the Italian campaign to another battlefield, with its own mountains. It might payoff in 1944 post Cobra when the forces in southern France would be better placed for pursuit but crossing the upper Rhine is much less of a problem to Germany than losing the Ruhr.