Control of the Mediterranean was vital. Control of the suez was vital. Without staging points in North Africa for the allied forces and with Control of the sea points from Gibraltar to the red sea the axis powers would have been able to hinder any southbound advance, as well as gain Iraq and the oilfields in the middle east as well as stop any Indian staging advancing.
Italy also were butthurt about the loss of Ethiopia and Germany had never been much of an expansionist during the age of empire. This would've solidified their Control over Europe, allowing them to focus on the Russian and British fronts more effectively, as well as provide vital resources for the axis war machine.
It was a pretty good strategy and vital to the long term success of the goal of a united axis controlled Europe. It just didn't work. Italians are terrible fighters.
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