No one said the US used nukes to spare Japanese civilian deaths. They did it to end the war which was killing thousands of people a day from both sides, and that was before an invasion that would easily kill over a million people.
The Japanese leaders still thought they could negotiate an "honorable" surrender that would allow them to keep the lands they had brutally enslaved.
They still believed in the Kamikazi, the "Divine Wind" which destroyed the invasion fleet of the worlds most dominant and brutal military machine just before it could brutally subjugate Japan. They thought they could arm children, the elderly, housewives, or turn them into suicide bombers and kill so many of the invaders that the bloodbath would force the US to agree to their terms.
US leaders really had no choice. If they tried to wait out the Japanese without using the bomb, the family of every sailor and pilot who died in those many months would be rightfully angry. They'd be out for blood against the entire sitting US government in the next election. Just as the families of the hundreds of thousands of dead US soldiers would be, after finding out the US invaded without using the bomb.
By ending the war more quickly with the bomb, US leaders also saved the lives of an immense number of Japanese who were being fired-bombed, shot and starving in huge numbers.
General US Grant was renowned for fighting brutal battles of attrition intended to bleed the confederate armies of soldiers, between his forces and theirs his battles created casualties of 350,000 Americans. But before he was given total command of US forces nearly a half million had already been killed. He ended the war after one last bloody year that was costing nearly 200,000 lives a year, and killing civilians by the many thousands.