Finishing the war in a way that Japan can't paint itself a victim.The Japanese were going to surrender, there were already talks of it. Generals and Admirals have since come out and stated that the dropping of the two bombs was absolutely unnecessary. The bombs were dropped solely to show Russia that we could do it.
But let's say for a moment Japan wasn't going to surrender.
So what?
Japan was decimated. They were arming their soldiers with sticks by war's end. So why invade at all? Just leave them there. Their infrastructure was destroyed and they had zero capability of pulling themselves back together anytime soon.
Dropping two atomic bombs seems like overkill just so we don't have to hear some bitching.