MAD was a dumb idea in the first place. Everybody has known, since the first world war, that a major power confrontation is very likely to end your nation, even if you win. The French were so demographically destroyed they literally could not raise an army to fight in the second world war. The British were so broke their empire collapsed. The Russian empire, the Austrian empire, the Ottoman empires all collapsed into splinters.

Rational people would not want to be on either side of such a conflict. Except, international relations is fraught with pathological incentives, so peer conflicts happen nonetheless, and less than twenty years after the first world war ended, everybody was gearing up for a second.

The cold war didn't go hot because we were lucky, not because MAD changed the basic dynamics of total war.