"being subject to nuclear devastation would have a lesser impact on the global economy, supply lines and climate than two major countries (State A and State B) being subject to nuclear devastation. Perhaps most importantly, the possibility of human extinction could be significantly mitigated if the target state refuses to retaliate. Surely the weight of human extinction would be a reason not to strike back."

The problem is that you likely don't have this "overview" kind of perspective of humanity as one giant species. If you had, State A wouldn't have tried to wipe out another country in the first place. Instead your stuck in a subjective perspective, where your own end is quite literally also the end of your world which for all intents and purposes is this world. So there is no "life goes on" (at least not for you).

Though while that technically also applies to your natural death and people don't usually go on a rampage when the doctor tells them their date of death. A) because it's still uncertain, B) because they are likely not capable of doing that, but mostly C) because there is no culprit and nothing they could do about it, also D) people around them will live on their memory will be preserved in whom they met what they did, what they build etc.

None of this would apply in this scenario, A) doom will be certain B) you are capable of doing something about it, C) there is a clear culprit, D) nothing will remain of you.

It's no longer about you it's just your decision to punish or pardon your murderer.

Though to individualize that scenario doesn't quite cut it either because it's not just your murderer but also a whole lot of other people not involved in that struggle or how much influence do you think you'd have on the pushing of the metaphorical button?

It's not even scorched earth, as that would also be "if I can't have it, nobody will", but it's a tactic to stop the advancement of an enemy by making an advance more costly due to removing the ability to live of the land and looted resources. While in this case you scorch the earth just out of spite, with no tactical benefit. Again with State A giving "good reason" to do so.

Some really twisted people might even argue with a twisted sense of pity, in terms of mercy killing based on the fact off how fucked up this would make those left behind, though that's always a very morally dubious argument.

However despite being essentially stupid and just spiteful to actually do, it's essential to pretend to do it in the concept of MAD.

So if the use of nukes leads to a massive retaliation and if that leads to MAD then you don't use nukes, right? ..., right?

Well the whole concept that bigger bombs make you safer is insane to begin with... The thing is what if one side uses nukes? Do you go all in and jeopardize all of humanity for one city or one army? I mean you could and your doctrine says you should but also that would be borderline stupid. But what if you don't do it? Does that make nukes ok now? Do you drop another bomb on another city or army to "get even"? Do you massively retaliate conventionally to the point where the enemy uses more "tactical" nukes in self-defense? How do you prevent that from being a precedent for the use of nukes? Like 1 is fine? Tit for tat? Only on military targets? Take out their means of retaliation? Just strike first and strike hard? A different non-military reaction?

Either way MAD does not prevent anything, if someone is willing to play a nuclear game of chicken mad is basically the option of just jumping over the edge, while not doing so sets you back to square -1 as you're not back to square 1 but even worse than before. Though again humanity is worse off than before a specific State A or B might still see that as advantageous to have dealt damage without consequences.

Also even if B is willing to go all in and communicates that intent, so is building a doomsday device that cannot be stopped by himself if set in motion by an attack by A. This would basically have the effect of most deterrents, at first it would deter an attack by A and after that it would trigger A's desire to defuse that doomsday device by all means necessary as one mishap on either A's or B's side could trigger the end of A and likely the end of the world as we know it. So B is quite literally sitting on a time bomb and it becomes paramount for A to either get rid of B or the bomb or both.

And the outlook that MAD isn't actually mutually assured destruction but that we would JUST makes this planet a lot less habitable for years/decades or centuries to come isn't really reassuring either...

So there are really no "good" options here, we will see it when it happens and that hopefully never will happen...