What you say is pretty much true except for the detonation of the "fat man" over Japan.
When I flew it was mantra that strategic bombardment from the air will destroy the enemy'e will to fight....but in Germany it didn't work at all.
What really nailed them was destroying oil and ball bearing manufacturing....when things can't roll or engines have no fuel the military has a big problem.
Have a nice day.
You need to check the history of Rolling Thunder in Vietnam. It was B-52s that brought Hanoi to the peace table. I've seen carpet bombing practiced on the live ranges out in Nevada. It's an awesome spectacle and it definitely affects the will to continue a war.
Nukes on the other hand are a political and psychological weapon. They are effective when used like the queen in chess. It's the threat of force they pose that gives them power.
GW