Nuclear war is not an extinction event, though. Most people would survive, and while they would face hardships, the "radioactive wasteland" thing is a fairly sloppy sci-fi trope.
That aside, if all nukes were launched, it's not about the directly irradiated areas. Imagine how much fallout will be launched into the upper atmosphere when 10,000+ nukes hit, with many in the multi-megaton range.
The sheer amount of material thrown into the air could virtually blot out the sun for potentially years. Given that a large portion will be radioactive, it could be raining death for years too.
Ehh the dust will fall out of the atmosphere within a few months. Large population centers will be craters proba ly. The 4 year nuclear winter will cause starvation and eating the "long pork" such that up to 90% of the population globally will die.
That aside, if all nukes were launched, it's not about the directly irradiated areas. Imagine how much fallout will be launched into the upper atmosphere when 10,000+ nukes hit, with many in the multi-megaton range.
The sheer amount of material thrown into the air could virtually blot out the sun for potentially years. Given that a large portion will be radioactive, it could be raining death for years too.