How do you avoid nuclear armageddon, when any single country's leader can trigger it?

MAD principle.

And well, in that case emissions globally would go down. So climate change would slow.

Part of MAD is predicated on concern about the thing being destroyed.

There aren't many countries run by dictators these days, but they exist.

I'd be a lot less comfortable in their making rational decisions not to use The Button. (After having moved their wealth and/or person offshore)

Does someone already running their country into the ground for personal enrichment, and vacationing in places {not their country}, really care about their country?