Isn't the real concern autonomous weapons?
Autonomous weapons, especially a nuclear arsenal, being used by an AI is a concern, but this seems downstream of the central problem of giving an unaligned AI any capabilities to impact the world.
Triggering nuclear war is only one of many ways a power seeking AI might choose to take control. This seems unlikely, as resources the AI would want to control (or the AI itself) would likely be destroyed in the process.
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