First off: Air superiority was not established easily or early over the continent. Also, Air superiority is not the same as air supremacy.
Second: Air superiority over the continent was established in part by gaining airstrips on the continent. Even after we established airstrips on mainland italy, we continued to suffer heavy losses of bombers, right up to 1945.
Third: The Italian air force, while unequal to the larger powers, was the least disgraceful arm of their armed forces. Bypassing mainland Italy would have kept Mussolini in charge, and the italian air forces in play, along with the german. Both had many rightly feared anti-shipping aircraft.
Fourth: there's the right angle problem. If a convoy is spotted heading towards its goal, it is relatively easy to intercept it, if the intercepting forces are coming from more or less a right angle to the convoy's path. If you leave the forces in the mountains unsubdued, they can act as spotters.
Fifth: While the Italian army was rather disgraceful, it still numbered around 3-4 million men. The surrender of Italy in 1943, in response to our landing on mainland Italy, led to the greater part of this army being demobilized, and a significant part to change to our side. Landing in southern France instead of Italy would have put this force on our flank, with the Germans dead ahead.
Sixth: The allies didn't have enough shipping to undertake two major landings at the same time. The landing that actually occurred in southern france was small scale relative to normandy, and used many of the same ships, sailed around to get there. If you put the first effort in the south, you would have to use MORE ships to get there, because of the greater distance. This would have meant FEWER ships would have been available for a normandy invasion, which would have to be delayed. So while it COULD work, you would be running the risk of having your southern France operation wiped out before you could even launch your Normandy operation.
As critical as I am of Churchill, I don't regard the Italian campaign, which he pushed for, as a failure. It did not amount to as much as he thought it would, do to his stubborn ignorance of geography, but it accomplished several important goals, including knocking Italy out of the war, securing the supply routes through the mediterranean, gaining airfields for the better bombing of southern Germany, Austria, and Romania, and tying down some german forces. It failed to be the 'second front' that Stalin demanded, but was a success as a diversion, and kept the enemy guessing as to where the next offensive would come.