Rising nationalism and games of "chicken" don't mix well.
[0]: https://www.popularmechanics.com/military/a23074/cuban-missi...
If a war had occurred, the US would have suffered enormously, but it would have come out of the conflict largely intact. Think the “get our hair mussed” bit from Dr. Strangelove.
The Crisis just shows that war can be avoided even when one side has a huge advantage, if neither side really wants it.
That made the situation even more dangerous than they realized at the time. The US would not have come out intact. It's very lucky for everyone that the Soviets decided not to escalate the situation.
Of course, I suppose MAD isn't MAD if there isn't also mutual knowledge of mutually assured destruction. It's something even worse when both sides think they have the advantage.
TBMs were another story, but there USSR had a sizeable lead in them.