I would feel a lot more secure in the efficacy of MAD if war was rational in the first place. History shows it is anything but.
It hasn't even been 100 years since the last nuclear weapon was used offensively, but already the world has come dangerously close to starting a nuclear war.
Numerous accidents involving nuclear weapons have happened. Critical and very dangerous errors were made in detecting that nuclear war had already begun when it hadn't. Countries with nuclear weapons have come close to going to war with each other (India and Pakistan, Cuban Missile Crisis). Weapon-grade nuclear material and nuclear weapons have gone missing. The American nuclear weapon launch codes were all 0's for something like 20 years.
It is an open question how a nuclear power will react to having a nuclear weapon exploded on their soil (potentially by terrorists under a false-flag operation) but it likely won't be a calm and measured response against the perceived perpetrator. If this happens in a poweder-keg like the Middle East, the ensuing chaos could easily draw in other nuclear powers.
Crumbling nuclear-weapons and launch-detection infrastructure in the former Soviet republics is still a major concern because of continued and increasing potential for accidental launches of weapons still aimed at their former Cold War foes, not to mention the renewed possibility of a second Cold War that has been in the news recently, and Putin's overt threats of the use of nuclear weapons.