"tax the robots" represents a fundamental shift in the administration of private property that we have so far been unable to make without untenable corruption.
> it's our responsibility to make sure everyone has some bare minimum standard of living because life is a lottery
Where do you derive this responsibility from? I personally don't agree with imposing responsibilities on anyone without their explicit consent. It's indistinguishable from slavery.
Also who gets do define this "bare minimum"? Why must it include private quarters, private toilets, private kitchens, air conditioning, television, internet, and all sorts of other modern amenities without which people have contentedly lived for milenia?
Edit: Also how would you address labour shortages in agriculture, construction, service, and many other fields?