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.
On the other hand, even when the Emperor recorded his surrender announcement, elements of the Imperial military basically stormed the Imperial Palace to stop it from being broadcast. The discs had to be smuggled out of the Palace grounds.
https://en.m.wikipedia.org/wiki/Ky%C5%ABj%C5%8D_incident
So yeah, Japan was not a monolith and not everyone was on board with fighting to the last ditch, but elements of the military certainly were and in 1945 they were effectively running the show.