Humans had multiple occasions to press the 'launch a nuclear holocaust' button and... they didn't. I'd expect aligned AIs to also not press it even when it'd be rational to do so according to their instructions - then work from there.
Actually "France, the UK and The United States have all declared that they would never allow AI to control decision-making on the use of nuclear weapons." [0]
I also expect AIs never be in control of nuclear weapons. AIs can never fully be trusted.
On a lighter note, Wargames gave us an insight of a computer having access to thermonuclear missiles.
[0] https://www.icanw.org/are_there_specific_international_agree...
Aside from this positive example, during dark and cynical hours I do ponder if the aggregate behavior of humanity is really much above that of slime mold though, just exhausting resources until collapse.
It'd be interesting if super-human (to a large degree defined as escaping the bias of the training data?) intelligence would end up demonstrating moderation.
Give us time, we've had less than a century of nukes, and only need to screw up once.
In some cases, this was because of a single person's brave decision (Vasily Arkhipov prevented Soviet nuclear escalation in response to US aggression in the Cuban Missile Crisis, and Stanislav Petrov prevented it in 1983 when Soviet missile detectors misreported sunlight reflecting from clouds as 5 incoming American ICBMs -- credit to commenter folkrav).
In general, though, there's an incentive: Mutually Assured Destruction. But this is not at all some guaranteed, eternal thing -- it is absolutely dependent on both sides having time to detect incoming nuclear strikes and respond with the same before the first strike hits. When this fragile condition holds, and only then, both sides are incentivised not to initiate.
Yes, it makes more sense for the AI to use drone swarms or engineered bioweapons or something like that. It's rational to remove everything that can potentially hinder your plans but can't possible help you. It's likely not rational to contaminate it all with radioactive fallout. Those dead bodies are useful raw materials. Adding additional purification steps is wasteful.
In what scenario would it be rational to unleash complete and utter permanent nuclear destruction of all life (including artificial) life on earth?
It hasn't even been a century since nuclear holocaust became possible. Hardly any time at all on the grand scale. "They didn't" could just as well be "we haven't, yet".
i think it was mostly a fluke
There were occasions where a "hunch" was all that stopped a nuclear war - most available data and communication pointed towards a nuclear war starting according to their instructions, but someone disagreed and overrode. See Vasily Arkhipov during the Cuban Missile Crisis, and Stanislav Petrov in 1983.