I like your WWII analogy, except for the fact that Britain would have fallen to Hitler, had we not joined the fight when we did. I think the scenario you proposed would have played out just like that, had our forces stopped at the Rhine.
Simply securing France, Belgium, and the Low Countries would probably have been sufficient to secure ours and our real allies interests. The Reds could have then taken over the rest of the fight, and Hitler and Stalin would have beaten each other to smithereens.
It’s interesting to war game out what might have been. I’m kind of turning your analogy over in my mind right now to see what lessons I can draw from it.
It would, of course, have been useful to have our forces nearby. If we put them in England, I don’t think the Germans would have invaded England to get at them snd they might have thought twice about the wisdom of running the risk of tangling with American forces in France, Belgium and the Low Countries. I am guessing that Hitler would have tangled with the soviets on the Eastern Front if it seemed that we would stay put in England or Western Europe. He was certainly a nutcase but why would he fight a two-front war if he thought it possible that he might fight only Stalin. We could have propagandized that our troops were in England only because of our old special relationship with the Brits. We could also have communicated that V-2s and buzz bombs were not welcome against our forces and might lead to quite lethal consequences for the nazi regime if indulged.