I have to comment that my father, who fought the Japanese through Burma & Malaysia (in The 14th under General Slim), showed no qualms regarding this action by the USA.
Of the very few things he ever said regarding his war experiences, the vast number of allied lives the two bombs saved (including his) was something he repeated every time the Hiroshima horrors were shown.
He hinted of seeing fanatical brutal Japanese soldiers in action, lost comrades, seen the Changi POW.
The idea of having allied soldiers fight on and on to walls of the Emperors Palace must have been a nightmare for Churchill and Truman.