It was one of the least militarized cities in Japan, which is why it had been so little touched by conventional bombings.
Not exactly. There actually was an important military base in the city (headquarters of the Japanese 5th Division and the 2nd Army Headquarters.), as well as many industrial targets, and it was an important port city. Keep in mind that Japan had converted most private enterprises and even many homes into places of war materiel production. There was no such thing as a non-militarized city in Japan at that time. Hiroshima, Nagasaki, and several other cities had not been bombed only because they had been taken off the bombing list some time before. The idea was to keep some prime targets "pristine", so accurate bomb damage assessment could be done afterwards. Everyone was well aware there would be massive civilian casualties.
Truman knew exactly what he was doing, incidentally. It was true he had moral qualms, but it was reported his Secretary of State told him "What will you say, Mr. President, at your impeachment proceeding, when the American people learn that you had a weapon which could have ended the war and did not use it?" The US leadership also feared the planned invasion of Japan by the Soviet Union, with the real threat of Japan being split into a communist and democratic zones similar to Germany. The bombing was seen as the quickest and surest way to end the Pacific war
Many in the US leadership and military brass had also been wildly optimistic about the "imminent collapse of Nazi Germany", after which the fighting had gone on for half a year still. History is fairly clear that the Japanese were unlikely to surrender before the bombing. Even after the two atomic bombs were dropped and the Soviet Union joined the war, the Japanese military leadership was still evenly split about whether to continue the war. It took the emperor to make the final decision. Even after the emperor publicly surrendered (without ever using the word 'surrender' or 'defeat' in his speech), a small group of Japanese officers actually mutinied and invaded the palace, fortunately not succeeding.