What was the plan to get over the Alps into France and Germany.
Italy invaded southern France in 1940 with a lackluster military - not a problem. In WWI Germany had to send troops to help Austria-Hungary defend the Alps (Italy was on the Western Allies side in that one), not a problem there, either.
The German defense of Italy (led by Kesselring) was simply a costly way to advance; they went to a virtually undefended Atlantic coast and opened up a second “foothold in Europe” instead. For all of the hype in the media, the Normandy invasion in terms of losses was much easier than many island battles in the Pacific; Americans were at the German border 3 months after landing. Guadacanal lasted longer...