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.
Not even arguing lives, you can't put your hindsight away for 5 minutes and consider the motives here and why Japan's terms for surrender were unacceptable. Amnesty up front for members of the fascist regimes is fucking insane. How would you feel about similar terms for senior Nazis? Both the WAllies and Soviets ended up letting nazis live after the war, but it was pretty essential they had full license to execute & persecute whoever.
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The terms they surrendered with were and had to be unconditional. Whether the nuclear bombs were necessary ** for that goal** is arguable, not the unconditional surrender. This is the only goddamn point I'm trying to make to you. My argument can be true and the nukes can still be wrong, these are not incompatible.