MAD works best also when you act as militaristic and insane as possible so the other side is afraid to do anything lest you kick the nuclear football. Hopefully everyone with access to the nukes knows this, but you cant admit you know this lest the enemy spies find out its a bluff thus weakening the bluff so both sides have to keep up the keefab at all time even internally. so while both sides may act like paranoid crackhead with a gun on the edge of starting Nuclear Armageddon for looking at them funny. They know its a suicide to actually fallow through. And it works. Why do you think the whole world puts up with the ongoing shit show in North Korea? They have nukes and can hit Tokyo Seoul Honolulu and Seattle.
Besides we don't even know that doesn't work. We haven't had a World War or major European war since the end of ww2. If we look back historically going 75 years without a major European war is amazing. all of the big wars since have pretty much been with major powers with non industrialized nations or collapsed failed nation states.
As for elites using nukes on the proles, that is ridicules and violates the don't shit where you eat rule. IE radiation poisoning doesn't care about your net-worth.