> Productivity improvements increase employment.

Sometimes: the productivity improvements from the combustion engine didn't increase employment of horses, it displaced them.

But even when productivity improvements do increase employment, it's not always to our advantage: the productivity improvements from Eli Whitney's cotton gin included huge economic growth and subsequent technological improvements… and also "led to increased demands for slave labor in the American South, reversing the economic decline that had occurred in the region during the late 18th century": https://en.wikipedia.org/wiki/Cotton_gin

A superhuman AI that's only superhuman in specific domains? We've been seeing plenty of those, "computer" used to be a profession, and society can re-train but it still hurts the specific individuals who have to be unemployed (or start again as juniors) for the duration of that training.

A superhuman AI that's superhuman in every domain, but close enough to us in resource requirements that comparative advantage is still important and we can still do stuff, relegates us to whatever the AI is least good at.

A superhuman AI that's superhuman in every domain… as soon as someone invents mining, processing, and factory equipment that works on the moon or asteroids, that AI can control that equipment to make more of that equipment, and demand is quickly — O(log(n)) — saturated. I'm moderately confident that in this situation, the comparative advantage argument no longer works.

No, Atlas shrugged explicitly believes that the wealthy beneficiaries are also the ones doing the innovation and the labor. Human/superhuman AI, if not self-directed but more like a tool, may massively benefit whoever happens to be lucky enough to be directing it when it arises. This does not imply that the lucky individual benefits on the basis of their competence.

The idea that productivity improvements increase unemployment is just fundamentally based on a different paradigm. There is absolutely no reason to think that when a machine exists that can do most things that a human can do as well if not better for less or equal cost, this will somehow increase human employment. In this scenario, using humans in any stage of the pipeline would be deeply inefficient and a stupid business decision.