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At one point during the war the British apparently received reliable intelligence that Field Marshal Kesselring was setting up his headquarters in a hotel that was right on the coast in Sicily and planned an operation to insert two dozen commandos by submarine to try and kill him and any other German officers they found in the thirty minutes they'd be ashore. The operation was put on hold however when the submarine was redeployed to attack a supply convoy and by the time they returned Kesselring had left.
So what happens if either the commando operation goes ahead beforehand or Kesselring stays longer and he's killed? As I understand things most of the senior military leadership back in Germany and Hitler favoured abandoning Southern and Central Italy to the Western Allies on the assumption that it couldn't be held without the Italian army, with it only being Kesselring offering his resignation in protest and arguing for a more forward defence that changed Hitler's mind. Here however he's not available to do so, and for the sake of this discussion let's assume his replacement follows orders and retreats to a defensive position similar to our timeline's Gothic Line. What does it do for the Allies to be able to make it all the way up to Marche and Tuscany much more quickly and with few casualties?