“Second, the labor share could stay non-negligible only because of a few top, say, entertainers, so that wages as a share of GDP fall indefinitely, as in a standard model of full automation, once these few are excluded.”

Well, if nothing else, you leave out sex-workers. That would not be just a few who you can meaningfully simply exclude.

And it’s not at all obvious that the number of “influencers” whom people trust and want to be in the physical presence of (some of the time) would be limited to just a few. But perhaps you’ll still say these entertainers collectively are a tiny number.

But human coaches / teachers (even if most are good because they best know how to leverage technology) are likely to be in demand, especially by parents for their children.

Physical therapists.

Human game shows with actual human participants.

None of this is to disagree with your assertion that the human labor share unlikely to go to 1, nor even to disagree that it is much more likely to go down significantly, but the idea that it goes to an extremely low level does not seem inevitable.

“Even in a perfect world, where everyone was equal, I’d still own the film rights and be working on the sequel” — Elvis Costello, “Every Day I Write The Book”