I think nuclear deterrence/MAD are actually downstream of the cause here.
Once sufficiently effective long distance military tools (bombs, missiles) could be produced at large scales, the defense equation was fucked. That happened before widespread nuclear weapon availability. If your peer adversary had the ability to spend debt on missiles, it was always an unaffordable, asymmetric proposition to counter that with a spend on missile defense. Sure, you spent some money on defense, but eventually the reality of the balance sheet became clear: damage at a scale that previously required your adversary to mobilize big chunks of their population in armed forces now just … cost money for missiles. And it would cost you much, much more than they spent to even semi-effectively defend against that. The opportunity cost of offensive action got massively reduced, IOW.
Nuclear weapons and other mutual-deterrence strategies emerged from that essential reality of modern mechanized warfare, they didn’t cause it. Once countries could no longer affordably defend against common attacks, they inevitably started looking for ways to deter attacks via incentive. The Cold War was the result.