Like you're indirectly acknowledging, the nukes had no real impact on their decision. Half their way cabinet wanted to fight to the last Japanese, half wanted to surrender. This was both before and after the nukes. The Emperor wasn't like a super-politician - he was seen as a [literally] living deity who was above politics. So the cabinet called upon him to make the final decision, which he had made long before the nukes - which was to surrender. There was no danger to him. Even the plots to undermine his decision involved destroying his announcement of surrender and leaving him under house arrest. And that plot was stopped by a speech from another officer, leading to most of the plotters to commit suicide for their dishonor.
And I don't think there were any real lessons learned. We nearly nuked ourselves during the Cold War multiple times. And today, with bombs that make Hiroshima and Nagasaki look like primitive weapons, you have people acting like nuclear war isn't something 'that' fearful. We killed hundreds of thousands of people largely for the sake of trying to get a slight geopolitical edge over the USSR. And that's far better than the alternative of there being no reason at all. In no world are the arguments about it saving lives valid, even if you attach 0 value to the life of the Japanese for having audacity to be born in the wrong country.
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Leo Szilard was a critical scientist in the story of the atomic bomb, and he's also full of just amazingly insightful quotes. [1]
- Suppose Germany had developed two bombs before we had any bombs. And suppose Germany had dropped one bomb, say, on Rochester and the other on Buffalo, and then having run out of bombs she would have lost the war. Can anyone doubt that we would then have defined the dropping of atomic bombs on cities as a war crime, and that we would have sentenced the Germans who were guilty of this crime to death at Nuremberg and hanged them?
- A great power imposes the obligation of exercising restraint, and we did not live up to this obligation. I think this affected many of the scientists in a subtle sense, and it diminished their desire to continue to work on the bomb.
- Even in times of war, you can see current events in their historical perspective, provided that your passion for the truth prevails over your bias in favor of your own nation.
[1] - https://en.wikiquote.org/wiki/Le%C3%B3_Szil%C3%A1rd