Points raised so far.
1. Only one nuclear bomber used per attack in Japan
For a start, the Americans had total control of the air. The Japanese did not have the fuel to get aircraft in the air. If the Americans had wanted to they could have used a pre-war biplane. If the Japanese had the ability to down American Superfortresses from the ground sucessfully, all the USAF would have done would be to mount a thousand bomber raid, and the nuclear carrier aircraft would have had a very good chance of being left alone.
2. Normal Bombing was more effective.
True, but it took time, and the defenders could fire back. Not so with a nuclear bomb. A single bomb could produce the results of tens of thousands of bombs, and there was nothing to be done. The mass destruction and sheer mental fear of a huge, city destroying bomb is bad enough.
3. Nukes and diplomacy.
America has the bomb. The Axis and Comitern should now be more fearful of America. Pro-Allied nations should start leaning towards America to benifit from this. Netural countries should lean towards or drift from the Allies depending on the average value of relations with members, to stimulate netural meduim powers being intimidated by this power and pushing against it.