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Why are options like dropping the bomb in Tokyo Bay, further off the coast, or in less populated areas not treated as serious alternatives? Why did the bombs have to be dropped on cities?To show their destructive power. That one plane could do as much damage as dozens / hundreds.
What would blowing up water show? What would blowing up an empty field show? What would blowing up an already-flatten city (like Tokyo) show? There is no shock value to dropping an atomic bomb on a non-target.
Arthur Compton, the scientist who led the plutonium side of the Manhattan Project recalled that:
> It was evident that everyone would suspect trickery. If a bomb were exploded in Japan with previous notice, the Japanese air power was still adequate to give serious interference. An atomic bomb was an intricate device, still in the developmental stage. Its operation would be far from routine. If during the final adjustments of the bomb the Japanese defenders should attack, a faulty move might easily result in some kind of failure. Such an end to an advertised demonstration of power would be much worse than if the attempt had not been made. It was now evident that when the time came for the bombs to be used we should have only one of them available, followed afterwards by others at all-too-long intervals. We could not afford the chance that one of them might be a dud. If the test were made on some neutral territory, it was hard to believe that Japan's determined and fanatical military men would be impressed. If such an open test were made first and failed to bring surrender, the chance would be gone to give the shock of surprise that proved so effective. On the contrary, it would make the Japanese ready to interfere with an atomic attack if they could. Though the possibility of a demonstration that would not destroy human lives was attractive, no one could suggest a way in which it could be made so convincing that it would be likely to stop the war.
Even with dropping the first bomb the Japanese War Cabinet wasn't willing to consider surrendering. It took two bombings for the message to sink in (and even then it was a 3-3 tie, and the Emperor had to be called in to break the stalemate): that is the fact any counterfactual has to contend with, that the two bombings barely got the ball over the line.
And even after the Emperor and Cabinet had made the decision there were still people willing to fight on and overthrow the government:
* https://en.wikipedia.org/wiki/Kyūjō_incident