My dad was an Army engineer in WWII, making sure the nickel mine in New Caledonia kept up production, in spite of the Vichy-leaning French governor there.
They were given orders to prepare equipment and personnel for the invasion of Japan. My mother-in-law, who is Japanese, was being trained at the same time how to use a bamboo spear to kill American invaders.
Truman made the right decision. Although a demonstration blast within view of the Imperial Palace might have worked just as well, the chosen strategy worked very quickly, ensuring the safety of both my father and my future MIL.
The thing is Tojo was plotting to kill Hirohito when he found out he was going to make his broadcast.