Whether to enter Europe from Italy in World War II has been a controversial topic. In Churchill's Memoirs, he speaks to this question many times. He complained that it was precisely because the Allies rejected his proposal to march from Italy into Europe that the situation after World War II was created. The dominance of the Soviet Union upset the political balance in Europe and resulted in the cold war.
The Allies expected that after landing on the Italian mainland, Italy was likely to withdraw from the war, so that the Allies could quickly invade the hinterland of Europe from Italy, attack the German mainland to the west, and cut off the german back road on the eastern front to the east, so that the German army on the eastern front was quickly destroyed by the enemy, and the German army on the eastern front accounted for more than half of the total strength of the German army, and once annihilated, Germany would undoubtedly be defeated.
The Allies landed in Normandy, and a large amount of supplies could be transported from England to Normandy. If the Allies had landed in Italy, allied supplies would have to be transported to Italy via the Mediterranean and under the threat of German submarines. In this calculation, the Allied supply lines would increase by thousands of kilometers, and Germany was best at submarine warfare, and once the Allies landed from Italy and Germany used submarines to blockade the Strait of Gibraltar, then the Allies were in a dangerous situation.
The United States wanted to land in France in 1942, and the two defeats at Dieppe and the Kasselring Pass woke up the Americans, and it was not so easy to fight with the Germans, which dragged on until 1944, after full preparation, the maximum concentration of superior forces, which launched the Normandy landing, in order to prepare for this unprecedented military operation, everything else had to give way, as for the Mediterranean strategy, let it be.