I agree with the overall message and conclusions of this piece, but I think there are two things that push against some of its arguments.
First, while I doubt that AI systems will be deciding whether or not to launch a first strike any time soon (for the reasons articulated above), I do expect leaders to use AI advisors to help make such decisions. Imagine you have the smartest political or military advisor there has ever been, an advisor with more knowledge than any human and an uncanny ability to predict future events and carefully weigh up the most complex decisions. This advisor is ever-present and responds to any question near-instantly. Maybe this system is not quite AGI, but it feels close. Is the person with their finger on the button really not going to consult this advisor? Not even as one advisor among many?
Second, I also have much less confidence that second strikes will not be automated using AI systems. Indeed, the Soviet Perimeter or 'Dead Hand' system sets a clear precedent for this idea. While this automated decision might be simpler and less strategic than others (Dead Hand was developed in the 1980s, after all), it still brings to the fore many of the concerns mentioned in this piece, such as issues with robustness.
I'd love to know what the author thinks of these points.