Fact: There was no world war.
Impossible to prove hypothesis: nuclear weapons prevented a world war.
Facing the facts about nuclear weapons means owning the good (probably prevented wars) and the bad (at the very least there were severe environmental and economic consequences).
There are direct quotes from Nixon and Reagan that claims this to be true. That is enough evidence for me.
In terms of cold war presidents itching to start wars, no.
Akshually there is, and WW3 has been going on since 2010. (Mostly in places that aren't Europe.)
War has still been going on since 1945, much earlier if not always, so akshually WW2 never ended or is just how it's always been? (mostly in places that are not "first world" / The West)
It worked.
If Stanislav Petrov hadn't been in the chain of command, MAD might not have worked. And it could still fail to work in the future.
https://en.wikipedia.org/wiki/1983_Soviet_nuclear_false_alar... https://en.wikipedia.org/wiki/Stanislav_Petrov