What was the purpose of dropping the atomic bombs in Japan?

The Japanese were pushing their eventual surrender terms prior to the dropping of the bombs. Before Nagasaki and Hiroshima it appeared the sticking point was that Japan wanted to retain The Emperor, but after the bombs dropped the US agreed to let him retain his seat anyway.

I've seen it said that the idea was to lead Japan to be more fearful of America than the closely approaching USSR, but the US had already destroyed 60+ Japanese cities through air campaigns.

Dwight D. Eisenhower

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I had been conscious of a feeling of depression and so I voiced to him my grave misgivings, first on the basis of my belief that Japan was already defeated and that dropping the bomb was completely unnecessary, and secondly because I thought that our country should avoid shocking world opinion by the use of a weapon whose employment was, I thought, no longer mandatory as a measure to save American lives

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William Leahy, Truman's Chief of Staff in July 1945

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It is my opinion that at the present time a surrender of Japan can be arranged with terms that can be accepted by Japan and that will make fully satisfactory provision for America’s defense against future trans-Pacific aggression

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It is my opinion that at the present time a surrender of Japan can be arranged with terms that can be accepted by Japan and that will make fully satisfactory provision for America’s defense against future trans-Pacific aggression

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Leahy in 1950

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It is my opinion that the use of this barbarous weapon at Hiroshima and Nagasaki was of no material assistance in our war against Japan. The Japanese were already defeated and ready to surrender….My own feeling was that in being the first to use it, we had adopted ethical standard common to the barbarians of the Dark Ages. I was not taught to make war in that fashion, and wars cannot be won by destroying women and children

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Major General Curtis Lemay

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The war would have been over in two weeks without the Russians entering and without the atomic bomb…the atomic bomb had nothing to do with the end of the war at all

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Chester Nimitz, Commander of the Pacific Fleet

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The Japanese had, in fact, already sued for peace before the atomic age was announced to the world with the destruction of Hiroshima and before the Russian entry into the war. The atomic bomb played no decisive part, from a purely military standpoint, in the defeat of Japan

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Richard Nixon on MacArthur

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MacArthur once spoke to me very eloquently about it, pacing the floor of his apartment in the Waldorf. He thought it a tragedy that the bomb was ever exploded. MacArthur believed that the same restrictions ought to apply to atomic weapons as to conventional weapons, that the military objective should always be limited damage to noncombatants…MacArthur, you see, was a soldier. He believed in using force only against military targets, and that is why the nuclear thing turned him off

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So why did we use it with such overwhelming military hesitation. Truman didn't consult with any of these individuals. Why didn't he?