You are correct, of course. But, that is the revisionist line lately taken by the anti-Americans who try to make the assertion that dropping the bomb was unnecessary.
Such a view is anti-historical and relies on a breathtaking ignorance of the times. To have had the bomb in 1945--and not used it--would have been an act of madness.
I am constantly stunned at how ingnorant people are of World War I and World War II. Many seem to envision WWII as a larger Vietnam War, not too big to be inconvenient, really.
It required everyone's contribution from the children who picked up recyclable scrap to the men on the front lines. We were fighting for our lives.