"In the long run automation ..."

In the long run automation will increase the share of income going to capital. I think theory is agnostic about how much this will happen when. Right now total wages as a share of GDP are down maybe 10-15% over the last 100 years, though it's possible that the human capital share is now a larger fraction of wages so that this understates the impact on unemployment.

If this process goes far enough, you do expect people to stop working (modulo psychological considerations), and to be supported either by investment income or redistribution. At the point when working full time merely doubles your income, it wouldn't be surprising to see many people bailing. Before that, most work may be collecting rents on human capital, which could also lead to unemployment for the same reason.

I agree that this is probably not what is happening now. I'm skeptical most of all because productivty simply isn't rising in the way this theory would predict. I don't see any way to reconcile the productivity data with the automation story, unless we posit some countervailing force that is significantly reducing productivity.