I think that the Allies would have come to terms with Nazi Germany. 1) My study has left me with serious questions about air power winning the war. The idea of breaking civilian morale didn't happen. Whether the Blitz of 1940, the 1943-45 bombing of German cities, the B-29 raids on Japan or teh V1 and V2 offensive against Britain the home front remained loyal. This was particularly true in Germany where the Nazi police state was busy hunting down traitors. 2) With out the demands of the Eastern Front I think Germany would have moved production from tanks and infantry weapons to airpower and missiles. They did a pretty good job of building underground facilities. SO there would be more defensive weapons available and fewer targets. Now by 1945 and 1946 there would have been a couple of A bombs available every month.. The first two at Hiroshima and Nagasaki were not opposed by any antiaircraft or fighters. 3) Once it was known what was coming there would have been furious attempts to intercept and destroy the atomic bomb carrying plane. Would this have been effective? I would think partially. I also think that that Germany would have responded with gas attacks. Remember Hitler didn't care about his own people.
IMO you're mistaken in your argument for two to three reasons;
1) Breaking civilian morale is one desirable outcome of strategic bombing and the one often trotted out, but it's arguably the least important of the two, with the other one being destruction of vital economic engines of production (factories, marshalling yards, oil refineries, communications nodes, and other industrial facilities). That is something nuclear weapons, especially against a target the size and target density of Germany, delivers in spades even at a pre-thermonuclear level. Germany didn't do
maskirovka, and their OTL strategic counter-intel efforts were so laughable that I don't see them mounting a successful target disinformation campaign. And the Volk may not break (under pain of Gestapo attention if nothing else), but it wouldn't matter once every city is either reduced to radioactive ash or starved of food and fuel due to that condition elsewhere. Civilian casualties would be ghastly of course, but this is total war against a blatantly proven irreconcilable foe, sometimes life sucks (besides, the Allies back then weren't as casualty adverse even if not utterly bloodthirsty, when a viable alternative is lacking). Of course, this is contingent on delivering bombs in coordinated mass strikes, not foolish onesy-twosy tit-for-tat raids and then waiting for a surrender that won't come. Two,
2) You say 'without the demands on the Eastern Front"... except the Eastern Front was never going to end in my estimation. This could boil down to differences in assessment, I grant you, but I'm of the "Russians won't ever stop" camp in terms of non-stop fighting along the Urals should Barbarossa be successful. That's going to tie down troops and resources, and that's assuming the Allies don't keep the convoys running (which the Germans historically could only intercept to a degree in the Arctic and Pacific) to arm the Rump USSR, which once pushed east of the Urals has a lot less far to go from Vladivostok to get guns and ammo to the front. It may not exactly be on the scale of US-UK convoys, but something to keep the Germans bleeding is better than nothing. Lastly,
3) The bomber will get through. It's as true now with suicide bombers as it is with aircraft, and while I've no doubt that the Germans will make serious efforts to shoot down atomic bombers once that cat's out of the bag, A) it won't be easy since air defense suppression is a thing that the US/UK would develop and perfect (they both did in short order in OTL), especially in the context of point 2 meaning Germany won't have All The Missiles for long, and B) it won't matter since the US is in an unassailable position to continue building more and better bombers and nukes that Germany can't directly stifle, or even match in production terms vis-a-vis interceptors/missiles against bombers. And if the Germans do gas Britain...well, like you said, that sort of thing tends not to work in cowing civilian populations, but rather bolster/harden their resolve.
The "win the war through air power" can work, technically, but it requires a level of willingness and ability to visit indiscriminate destruction against the opponent until there's no credible resistance left to offer. We don't see that (thank God) in OTL, but it's possible once you decide to cross that line. And against Nazi Germany, I can't picture a more justifiable target of that abuse. The question I have is would the Allies reach that point and decide to pull the trigger; I have my doubts, but I think it's at least plausible depending on how surrounding events unfold. The issue is that Nazism is not a good stand-in as an ideological backbone (compared to Communism) for a stable Cold War to unfold against the West, so some form of conflict is likely without a radical (IMO 'Notsi' level) shift in the Reich's foreign affairs policies.
EDIT: For the sake of clarity, I'm operating under the assumption of a AANW-esque scenario, only I don't believe the Soviets would've surrendered or sought terms under any circumstances, hence my stance of a conflict that waxes and wanes, but never actually stops on either front.
