When you are in a fight and you beat the other person to the ground, you ask them to give up. If they do not, you knock them to the ground again.
Finally if they don’t give up, you make it so they are no longer a threat.
Go back and read the NY Times from the past few weeks (in 1945) it was clear that Japan was beaten. They had been given several ultimatums. They refused to surrender.
If we let them starve, millions would have died and the long term effect would be horrible. By using the bomb we gave the emperor an out. There was no way to defend against its use, therefore no one was to blame for the defeat. Everyone retained face. They could accept peace with honor.
War sucks. But it was a risk management exercise. The cost of maintaining a standing army waiting for millions to starve and then invading versus killing thousands, getting a complete capitulation and a pacified population. Sometimes you have to accept the least bad choice.
So if the Japanese hadn't surrendered after Nagasaki, the U.S. would have been justified in bombing every Japanese city to ashes in succession -- until there were no more Japanese people left alive?
What you've presented there is a case of post-factual justification using a rationale that only works in hindsight. Because the Japanese surrendered after two atomic bombs were dropped (as opposed to 50, 100, etc.), we can look back and feel vindicated that what we did was right.
Six of the seven five-star generals and admirals of that time believed that there was no reason to use the atomic bombs, that the Japanese were already defeated, knew it, and were likely to surrender before any American invasion could be launched.
For morality, I consult God's law.
For military strategy, I consult military leadership.
In this case, they pretty much agree in their conclusions.