To be cold blooded about it, we could afford to have multiple divisions in an Italian quagmire as long as the German were resisting. Just as the Soviets seemed to have an inexhaustible supply of bodies to put in Red Army uniforms. The Germans had a big problem in the east and were anticipating one in the west. Every German fighting in Italy reduced the number available to meet those problems by one.
Help the Russians. Help the Russians. When the Germans tried to get us to join with them against the Soviets (after we had severely thrashed the Germans ). We should have taken them up on it. Patton would have.
Ah... Shoulda Woulda Coulda
And hey! The Italians couldn’t wait to join us and hang Il Duce by his nards. (If they were any help)