So, what happened? One answer is that the atomic bombs were dramatic enough to shift the balance of political power in Japan.

Yes, generally it is believed that just before the atomic bombs, Japan was defeated, knew they were defeated, were out of oil with no chance of getting more, short of food, etc. and were interested in negotiations to end the war. It appears that then the US insisted on something really simple, definite, final, humiliating, etc. -- "unconditional surrender". In the end Japan did get to keep their emperor which was good for the US since it meant that the US occupation of Japan was easier -- just work with the emperor instead of civil war in the streets.

Drama or not, the atomic bomb was darned scary -- one bomb, one airplane, one city, and the fire bombing was not nearly that powerful, that is, required lots of airplanes.

I don't know how many bombs the US had ready then, but Japan could fear that the US could destroy a city a day, including Tokyo.

But this is a bit off the subject: If you don't like the atomic physics, math for the critical mass calculation, the shaped charges, etc., then pick GPS, radar, penicillin, the SR-71, and the transistor as examples of where wildly successful projects were based on science, math, and engineering, proposed just on paper, and could be and were accurately evaluated and funded just from the paper.

And whatever Japan's response was to the atomic bombs, the bombs do illustrate one of my points -- they were evaluated, justified, and funded just from paper and worked as predicted.

Also notice that the US has lots of long range missiles with warheads based on nuclear fission and fusion but not based on the firebombs.