Normandy 1943.

If the allies do not destroy the DAK, then they must detail forces to maintain the encirclement, including naval forces for the blocade.
Which existed. Which would be fewer in number than OTL destroying them. (On land, at a minimum. I'm willing to bet the sea & air components would be smaller, too. It's not like the Germans had control of the Med & could pull their own Dynamo...:rolleyes:)
If they do not take Tunisia they can not use it as a launchpad for the invasion of Sicily. Instead the invasion will have to be launched from a more distant location which instead will cause some problems, especially in the area of aircover.
Which doesn't make it impossible.
By loosing Italy the Germans not only lost the Italian soldiers that would have fought on their side otherwise, they allso lost the German troops they sent there.
Conceded.
The Italians could defend on their own against commando raids, and with troops to spare. And even if the Germans have to send troops to Italy, as long as these are not engaged in actual combat they do not suffer losses and are thus a smaller drain on Axis resources. Also, garrison troops can be of lesser quality compared to what the Germans sent to Italy in an effort to stop the allies.
Conceded. Nevertheless, they have to be supplied, which is a drain Germany really can't afford. Germany also has to supply the Italians in large measure, which wasn't the case after the Allies invaded. And all the Italian civilians. It's not all about troop numbers. It's about logistics.

Beyond that, the continuing presence of German troops won't necessarily produce happy feelings among the Italian public.:rolleyes: (IIRC, they were none too fond of the Germans OTL. Even less so, I bet, after they've bounced Mussolini into the street, thought the Allies were coming to help, & seen the Germans come back.:eek:) Nor will repeated commando & gunboat strikes all over the damn countryside every night (nearly every?) bring tidings of joy for the German presence.:rolleyes: I'll wager propaganda leaflets encouraging Italian resistance & sabotage will turn up. Maybe we'd even see an Italian Resistance. (Is that an oxymoron?:rolleyes:) Still think the Germans are better off?
The Italian campaign was a drain on allied resources but it was allso an equally large drain on Axis resources, and the allies could better aford it because they had reserves.
By "spending" troops and equipment in the Italian campaign, the allies managed to weaken the enemy before the actual decisive battle, in France.
That's the conventional wisdom. It's false. The Allies had about twice as many men in Italy as the Germans, & the Allies were also supplying the Italian civilians. It's not only a military issue, nor only troop numbers. It's total logistic demand.
All I know is that in OTL, the allies never managed to completely stop the Germans from redeploying troops to a certain front, wether they tried it or not. The allies could delay the movement of German troops, not stop it completely.
In Normandy, they came as close as they needed to. I see no reason they couldn't duplicate that effort, especially if they added in attacks on canals & mining ops. Would it be easy? No. Possible? Yes.
 
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