“What happens to “capitalism” when the costs of production approach zero (in other words, when amassing capital is no longer necessary for the production of goods)?”
IMO, we already got a hint of the future during the China expansion.
Wages go to zero. Demand for raw inputs will increase. Property prices go through the roof. Commodity prices go through the roof. All those robots won’t be “cheap”, either. They will be the only real form of capital, and the pseudo-aristocracy will do everything they can to keep them out of everyone’s hands.