I don't think it's actually possible that actual anarchy would lead to more advanced capitalism immediately superceding it.

Today's capitalism is only possible through the large amount of complexity our system can manage. A collapse is sometimes defined as a rapid simplification of a society...in a collapse scenario...I don't think we'd be able to have three different payment mechanisms for one card, international credit organized, or software as a service models. If the instability of the US causes it to go to anarchy, nobody will give a shit about evil corp's business model and its corresponding license agreement. If they need to break it to eat, they will. They'll break it so often that it might as well not exist.