What purpose, realistically, would have been served by attempting to invade the continental U.S.? The fall of England would not have suddenly resulted in Nazi

What purpose, realistically, would have been served by attempting to invade the continental U.S.? The fall of England would not have suddenly resulted in Nazi possession of Canada or Britain's Caribbean possessions. Trying to launch operations at the bitter end of a trans-Atlantic or trans-Pacific sea-borne supply line would be fraught with risk. In the Pacific, the U.S. never really faced the bulk of the Japanese Imperial Army, which was largely tied up in Manchuria, China, and south-east Asia. Pacification of China would have been a long, drawn-out affair under the best of circumstances (with regards to Japanese imperialism). One of the more interesting what-ifs, I think, is what would have happened if the Japanese Army faction had won out over the Naval faction, and an attack was launched towards Siberia, rather than against Hawaii, the Philippines, and Indonesia in 1941. This would have conceivably tied up a significant portion of the experienced Soviet forces that were shifted from the Far East command (including a particular future field marshal) to help blunt the German invasion at the gates of Moscow.