They dropped two nuclear bombs on Japan to make the Soviet Union's invasion of Hokkaido unnecessary and as a performative act to horrify the world in to subjugation.
The whole 'saved more lives than it cost' is a bad argument unless the plan was to slaughter a hundred thousand civilians on landing. Note the Nazi invasion of France cost 60,000 lives in civilian resistance...this was at the beginning of the war.
Japan would have surrendered on the first day of invasion.
Yeah and that's all correct, I'm just arguing that the reason for the bombs was not a proto-cold war move against the Soviet Union. I don't think the bombs or any targeting of civilians were justified at all, but arguing the proto-cold war reasoning is something leftists tend to zoom in on too quickly without researching, it is ahistorical and adds a layer of hindsight bias coloured by our own leftist bias that simply isn't necessary in order to to condemn the bombings.