Where did you get the idea that the USA was “eager” to deploy the atomic bomb?
>Stimson wrote in his diary afterwards that after his briefing, Truman felt “the terrible responsibility that such destruction placed upon us here and himself.” [1]
[1] “Memorandum of Conference with the President, August 8, 1945 at 10:45am,” in Stimson diary (8 August 1945), Henry Lewis Stimson Papers (MS 465), Manuscripts and Archives, Yale University Library.
For starters, how many days did it take before we dropped the second one again? I don't think it matters what any of the participants wrote or said given the events that we know to have transpired. There were clearly many other paths available to take.