I think the sentiment at the time was that when we were done with Japan, "The only place Japanese will be spoken will be in Hell."
Dropping those two A-bombs on Japan saved the Japanese people from total annihilation.
They wouldn't have given us the choice. The would have fought to the last man, woman, and child - that's how that society was. The only way to subjugate the Japanese would have been to kill them all.
The A-bomb shocked them out of that mindset. They realized that we could just sit back and incinerate their homeland, their people, and their Imperial family, and not have to risk any infantry. There would be no Americans in reach to take with them to the afterlife.