In several decades of seeing stray discussions online about nuclear war, including here on HN, I've yet to see a discussion where human extinction wasn't a commonly assumed outcome.

It's almost always thrown out as a matter-of-fact inevitability, it's assumed. It appeals to the self-hating cult of 'humans deserve it.' I'd wager the people that float that theory more often than not tend to hate humanity and are lusting for its destruction, so that appeals to them, they want it to happen and are projecting irrationally outward.