Eliezer, there are at least six comments on that directly. They also make the point that you have not addressed: they believe that the world may be safer because of using a pair of relatively small nuclear weapons. The main arguments for that side have been that we really did need to see the ruins and that MAD was necessary once multiple parties had nuclear weapons (nothing says MAD like someone showing they really will do it). I may take as a separate point that we would not have worried so much about proliferation, particularly by smaller-than-state entities, if we had not seen the effects. Against that, you have a norm of "impolite" nuclear weapons and a concern about hypocrisy?
As you say, the p-value could be tiny and still meaningful, and your follow-up comment seems more certain of the sign on it. There are also several comments on that point: people seem very sure in hindsight what decisions should have been made decades ago. This is odd whether the argument is that this was the only possible way or that it was completely unnecessary because we have had no other nuclear weapon use since then.
To put it differently, was a "first time" inevitable? Arguable. What would have happened if that first time came when more and/or more powerful weapons were available? Very bad things. How certain are you (general you, anyone) that this was not a 200,000 death innoculation against the 1 billion death war? I am not 99.98% certain that the bombings made future bombings either less or more likely.
Which I suppose is a separate argument against: if you are not 99.98% certain that your decision will prevent 1,000,000,000 deaths, you probably should not kill 200,000 people based on that decision. Which I suppose is a separate argument for: if we are less than 0.02% certain that there are long-term effects in any direction, short-term concerns dominate. (I'm not fond of the latter, phrased that way, but this comment is long enough.)
On August 6th, in 1945, the world saw the first use of atomic weapons against human targets. On this day 63 years ago, humanity lost its nuclear virginity. Until the end of time we will be a species that has used fission bombs in anger.
Time has passed, and we still haven't blown up our world, despite a close call or two. Which makes it difficult to criticize the decision - would things still have turned out all right, if anyone had chosen differently, anywhere along the way?
Maybe we needed to see the ruins, of the city and the people.
Maybe we didn't.
There's an ongoing debate - and no, it is not a settled issue - over whether the Japanese would have surrendered without the Bomb. But I would not have dropped the Bomb even to save the lives of American soldiers, because I would have wanted to preserve that world where atomic weapons had never been used - to not cross that line. I don't know about history to this point; but the world would be safer now, I think, today, if no one had ever used atomic weapons in war, and the idea was not considered suitable for polite discussion.
I'm not saying it was wrong. I don't know for certain that it was wrong. I wouldn't have thought that humanity could make it this far without using atomic weapons again. All I can say is that if it had been me, I wouldn't have done it.