The Amercans used the bomb for reasons other than to defeat Imperial Japan, but to signal the Soviets not to invade Japan. They (U.S.S.R.) already amassed thousand of troops in Manchuria waiting to land on Japan at that time. The US developed the bpmb ahead of all its enemies, so it was necesary to show the world that they had that weapon. And would use it. If they had to. That is history.
Cheers!