Sicily and the Italian campaigns had as much to do with political considerations as strategy. The Allies couldn’t leave the fighting to the Russians while waiting for the main invasion in France, and they had two armies in the Med with nobody to fight. Perhaps if they had ignored the political issues and those divisions in Italy had been at Stalingrad instead, the fight on the Eastern Front would have been more drawn out, but when you have allies, you often have to do things more for their benefit that your own.
Yeah, allies. That’s the ticket.