The Japanese propaganda machine had told the Japanese people that the Americans were "devils" and that they would rape and kill all women and children captured alive. The reason that the atomic bombs were dropped were largely because the loss of life due to an invasion would have been extremely high, as the Japanese were fighting to the last man for the most part, and civilians were also not surrendering in droves (see: Midway). On top of that, consider that just a year earlier the allied forces had learned what a large cost coastal invasions had, with the Normandy invasion, Operation Overlord. The bomb was used for threefold effect: Shock and awe as an attempt to force immediate surrender from Japan, a warning to the rest of the Axis forces that had not yet surrendered (small pockets of resistance), and as a power play to show that the US had amassed weapons beyond the capacity of the rest of the world. When Japan did not surrender immediately as a result of the first bomb, the second was dropped. It doesn't matter if Japan was fucked. What mattered was ending the war as fast as possible and restoring peace.