If you ask what the known U.S. procedures and plans have been, the answer is a resounding YES, they would have nuclearly attacked ALL their enemies at once according to the man whose job was to evaluate these procedures and plans of the U.S. military:

https://www.bloomsbury.com/uk/the-doomsday-machine-978140888...

Just a sample quote:

"I soon discovered that in the plans of Pacific forces, from top to bottom, there was no provision at all for attacking only the Russian targets in their sphere. In every plan for war with the Soviet Union, Chinese targets (including every major city in China) were also struck."

In the whole book there are many accounts on that, on the various levels of the chain of command, even intentionally designed to act independently.

More transparency is still needed there, probably much less was changed in the following years than it ever admitted to any civilian, including the presidents, again according to the book, so the state is more than scary and when I read that insider info, I consider these involved really completely mad. Most of them Nazi-like "we just follow the orders" mad, and some simply pure evil mad.

Similar to the cyber attack attribution problem, isn't it?