Humans don’t always do what is right, what is best, what is the most practical. It could be argued that they seldom do. Furthermore, what makes ‘sense’ is usually something that is purely subjective from the point of view of those making the decision at that time. Humans and their societies tend to follow patterns of behavior as much as anything else.
Because of that, since an economic crash is a mathematical, foregone conclusion, what history shows is that the likelihood of a major war breaking out, even a world war, is very high.
Keep in mind that those Cold War nuclear arsenals are still there, the nukes have gotten more accurate, and more countries now have them.