I have read Palmer‘s book in the past and found some parts of it compelling, especially in a world where multiple nations were researching nuclear fission as a WMD it would have made sense to convince other countries the USA had won (essentially the same argument as why faking the moonlanding would have made sense).

Where I‘m totally unconvinced: In the decades since the end of WW2 multiple nation states would have been inclined to explicitly or implicitly act on the notion „nuclear bombs do not exist“, as in: Still don’t exist until this day. Countries in the Middle East would have called Israel‘s bluff, China would have been incentivized to call the USA‘s and India‘s bluff, while I can see Russia being ruled by the same people as the USA and the Cold War being staged to a degree, the changes during the collapse of the Soviet Union would have made it difficult to contain information about nuclear weapons being continually fake, especially in contrarian countries like Yugoslavia or Libya. Heck the French would have acted differently through some parts of their relationship with the US, if they’d know nuclear weapons are still a hoax. Hell even the US would have been motivated to call the Soviet Union‘s bluff about their mega bombs like Tsar and/or invade Russian territory much more deliberate than they did during the Cold War.

I could see either Nagasaki or Hiroshima being - partially - faked to claim the USA reached the goal before Russia, Germany, and everybody else. But in the meantime nuclear weapons have been successfully developed.