A whole country the size of the US can crap its collective pants with a freak cold snap and you think 10^4 nuclear detonations destroying all major cities is quite survivable?

The initial fission stage is the "hard" part of a nuke, but the subsequent fusion stages are much easier to scale up. Arbitrarily large nuclear bombs are theoretically "easy" to make by chaining increasingly large fusion stages one after the other, as they aren't limited by expensive fissile material.

https://blog.nuclearsecrecy.com/2012/09/12/in-search-of-a-bi...

Hence scientists extrapolated nukes really could end life on Earth, and in a slightly different reality than ours, they may have.

What about Nuclear Winter?

Correct.

https://www.navalgazing.net/Nuclear-Weapon-Destructiveness

> To put this another way, each bomb can destroy an area of 34.2 square miles, and the maximum total area destroyed by our nuclear apocalypse is about 137,000 square miles, approximately the size of Montana, Bangladesh or Greece.

(I think that should be Bangladesh and Greece; Montana is larger than the two of them combined.)