First, history of the past 80 years casts doubts on your claims:
The USSR-Afghanistan left an estimated 2 million dead. Nigerian Civil War between 1 and 3 million. France-Algeria War about 1 million. Korean War between 1.5 and 4.5 million dead. Vietnam between 1.3 and 4.5 million. I could go on really.
MAD doesn't stop wars from happening. It only stops nuclear powers from using nuclear weapons. And it stops major powers from targeting each other directly. That's the extent of MAD. Even that's a contentious claim to make: Pakistan vs. India over Kashmir comes to mind.
Even more so, MAD isn't the only incentive for not going to War. After World War II, the World got profoundly reshaped with new economic and geo-strategic treaties and alliances. Bretton Woods, United Nations, NATO, European Union,... come to mind. In fact, after 1945, European integration was considered as an antidote against extreme nationalism in Europe and was heavily advocated for by Churchill.
Second, "global casualties from warfare being in decline" doesn't imply that no casualties of war, or atrocities, have been committed since 1945. Neither does it imply that things can take a turn for the worst without resorting to nuclear weaponry. For instance, the Syrian Civil War sits at about .5 million dead currently, and it has essentially been a proxy war between regional as well as global powers. And let's not forget the Ukraine situation that's currently playing out.
Third, the "lack of a contingency plan" is essentially part of the Prisoner's dilemma which the arms race during the Cold War was: https://en.wikipedia.org/wiki/Prisoner%27s_dilemma#Internati... But that doesn't render the argument moot: objectively, casting nuclear weapons out of this world is the best outcome for everyone involved. But rationally, that's not possible as you end up in a situation where owning nuclear weapons while everyone doesn't is the better option from the perspective of a single nation. Albert Einstein was well aware of this dilemma and said he wouldn't have participated in the Manhattan Project if he had known that the German bomb was a figment of imagination.
The main reason why MAD has become a thing is because a chunk of humanity just wants to see the rest of the world burn. No matter how rational and bent on peace between nations you are yourself, you can't possibly predict whether the other side has equally rational leaders or, as it turns, absolute mad men behind the buttons who are very much willing to use them when push comes to shove. And that's absolutely not a great outlook for humanity in the long term. We're extremely lucky to not have had a war between major powers over the past 80 years; it's been a close shave a few times as well (e.g. Cuban Missile Crisis).