The reasoning at the time was that the Japanese would not believe the U.S. could do it more than once and they would have to believe the U.S. could obliterate Japan in order to surrender.

I have no idea if that would have been true, but that was the idea. It certainly is true that the Japanese were being told to fight until every last man, woman and child on the islands died, so it was a desperate situation all around.

But the fact is that it was only a matter of time before someone developed an atomic bomb and no one has been crazy enough to use one in a war since 1945. The main reason for that, in my opinion, is that the world saw what happened.