Even in general, socio-economic models are not of the same quality as the physics models (and no-one is making that claim anyway). The SSPs are more like share narratives rather than forecasts.
You know that humans do have nukes, right? And a long history of killing each other over pretty much anything? (from land rights to idealogies and everything in between).
So in your estimation, who would be a good source to determine how/whether humans get to a point where nuclear war is a likely scenario?
Why the obsession with nuclear war and trying to get totally imprecise scenarios there? They serve very little purpose other than building scary narratives. Some people's job is to worry about them, but that doesn't mean they are central to what we should do.
When a hurricane strikes, things are usually not just Lord Of The Flies - the idea of collapse into violent chaos is a popular one but doesn't really happen much.