Dropping a nuke on Tokyo might have made things worse.
If the Imperial Palace had been blown into a dust strewn moon scape the Japanese would have assumed that their beloved Leader had merely taken his palace and servants and assumed a place in their version of heaven.
They would have fought like mad men until the island had been cleared of human life.
It would have cost millions of lives, just on our side.
Most Japanese had never even heard the Imperial voice until Hirohito recorded the radio broadcast announcing that Japan would surrender.
The only reason the surrender and occupation went as smoothly as it did was because it was an Imperial Decree that the Japanese would be subject to rule and oversight by the allies.
Which was why Tojo tried to kill Hirohito before he could make that broadcast.