Consistent with your scenario, Admiral Rader advocated that Germany seize Gibraltar, the Med and North Africa, and Egypt, then extend their forces down the east coast of Africa and interdict the flows of Mid East oil and Allied supplies to Russia, and sever England’s lines of communication with India. This would have accrued substantial gains for Germany and Japan, potentially to the point of knocking Russia out of the war. If so, Germany’s position as supreme in Europe would have been secure.
But he didn't. As he said in Mein Kampf, international Jewry and Bolshevism were his mortal enemies, not the Anglo Saxons. So he continued prosecuting the war on Russia to the demise of his nation.
“...Admiral Rader advocated that Germany seize Gibraltar, the Med and North Africa, and Egypt, then extend their forces down the east coast of Africa and interdict the flows of Mid East oil and Allied supplies to Russia, and sever Englands lines of communication with India.”
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An excellent point, and the Admiral wasn’t so far off the mark. Of course, the problem was that Hitler and Army generals could never quite grasp the ‘big picture’; German military thinking was, and had been for centuries, confined to land warfare against their neighboring countries. Therefore when Raeder presented his tours d’horizon, the reaction of Hitler and the Army staff would likely have been something like, “Huh?”