Unfortunately, the worst days of the cold war were appreciably less likely than we are now to immolate all of mankind. In 1963, the two nations capable of global annihilation were run by “company men” who acted with caution and tons of input from myriad experts who knew the real cost of global war all too well. Those bureaucrats understood that their rash act would end their “life at the top” in a heartbeat, even if they survived nuclear armageddon. But today's strongmen/ dictators who control nuclear weapons have shown far less cluefulness or concern than their forebears for the very plausible dangers of committing a single stupid blunder that could end life on Earth. Hard to be upbeat given that, regardless of appeals to rational technical optimism.
There are more players now but I don't think the cold war Soviets were as stable as you're arguing here.
We've had mad men with nuke since we've had nukes. The more time we spend in that situation the higher the chances someone uses them but I think we're far safer now than times such as the Cuban missile crisis. The Soviets had their nukes on a dead man switch. That was insane and could have killed billions accidentally.