I don't understand how the annihilation of humanity is justified/not insane in that scenario. Hasn't the world basically already ended? What's the point of ending it more at that point? It's like fulfilling a contract for someone you've already killed. You've made a promise but there's no need to keep it.
The concept of MAD rests on the assurance that the launch orders will happen. If there is no execution, the system falls apart. Answering The Day Three Problem makes Day One vastly less likely by creating a situation in which no successful preemptive strike is possible. But, more to the point...
Winning and losing at this point are more than a little relative terms, but being able to win Day Three (in effect, still being able to issue orders to your remaining strike forces and having remaining strike forces) effectively negates Day One and Day Two as an option for your opponent, for
any opponent. There's nothing in the cards for engineering a war between the superpowers now either. It will only buy you annihilation in nuclear fire.
This is MAD at it is most fundamental, its most important. Nobody has anything left to gain, not even the neutrals and the fifth-tier who'll never be targeted. Nobody with delusions of grandeur and one or two faithful men can start a nuclear war now, just as the major players cannot. Like all MAD, it's in the hope of never executing. This does not change the fact that to be effective, it must perform as advertised.