Good points other than that nuclear winter isn't real.

The fears were based on preliminary concerns and math exploring the idea, and spread for political goals. They also assumed a total exchange when there were far more nukes in the stockpiles, but deescalation worked and there are simply not enough nukes to trigger it anymore.

There are still concerns about a "nuclear autumn" but I don't think OverlordGPT would be that worried about it as long it has become materially self sustaining, but that's presumably somewhat difficult.

Really, the scary thought is that maybe OverlordGPT might start a nuclear autumn on purpose.