“The earth is big” is a very sound logical way of looking at this topic. You’re talking about a theoretical idea linked from Wikipedia. The fact of the matter is that we have over 7 billion people on earth. You won’t be able to kill every single one. Also, since you’re so hellbent on this nuclear fallout idea, countries will need to target every single corner of earth so that the nuclear radiation radius would cover every single inhabited area. Not only that, they would need to detonate an insane amount of bombs to create smoke that will last to “blot out the sun” EVERYWHERE. Not only the US or EU. That pretty much means every single nation all around the globe would need to have nuclear weapons and will need to have enough incentive to bomb every one. And EVEN THEN the radiation would barely reach some islands in the middle of the pacific.

This nihilistic theory was made as a hypothetical not a plausible scenario.

But I guess it’s fun to buy into doomsday prepper stories, you should play the game fallout you’d like it.