The DAK was never a large force. Had Britain defeated the Italians quickly, then that theater of operations would no longer be a viable one, as the British would rule the sea. Overall, though, I don't see the outcome of the war being affected very much.

Although we might have seen something like this:

1) Italy with the help of Germany starts
setting up a comprehensive defense
of mainland Italy, making any Allied invasion
that more difficult.

2) Not having North Africa as a training ground,
and Italy being fortified, the Western Allies
put off opening a second front, possibly
allowing the Soviets to gobble up more of
Europe, and maybe shifting more war material
to ETO, delaying some action in PTO

As for Rommel, I too see him serving in the West somewhere.

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