However, it probably wouldn't have changed anything because Japan did not surrender even after Hiroshima,
And I agree with you that it was the correct thing to do and no one should ever have any doubts about the decision.
That would have been a waste of a bomb and it wouldn't have done anything to motivate the war faction within the Supreme Council for the Direction of the War to end the war. It also most likely would not have swayed Hirohito to break the tie, which occurred after Nagasaki. Hiroshima could be quantified and it showed American resolve.