It's interesting: Thiel's "truth that few people agree with you" is that capitalism & competition are antonyms, not complements. And he's in favor of the "capitalism" side. His whole business career is about eliminating competition and enjoying monopoly rents. A return to "kings and aristocracy" is the ultimate culmination of this: a king has ultimate monopoly power over the kingdom, where they not only own all the land, but have ultimate say over everything that goes on in the kingdom.
There's an opposing side to this dichotomy though: embrace competition. American democracy, with its separation of powers, is an example of this. The founding fathers explicitly set the government at odds with itself, because when "ambition is made to counteract ambition", the ambitious are so busy fighting each other that ordinary businessmen and citizens can go about their business relatively unmolested.
To answer your question: I'd absolutely work for an anarcho-tyrannist firm where I have no idea who the CEO is and managers can fire me on a moments whim, as long as I can walk into another firm tomorrow and get a new job. Job loss is only traumatic if all your eggs are in that one basket; if there's always another job waiting for you, just go get fired and take it.
The separation of powers could be expanded to a far greater extent. In particular the modern bureaucratic state, with its long-term sinecure positions at the highest levels, is entirely antithetical to the whole idea of checks and balances, or "ambition being made to counteract ambition". This is where former aristocracies might provide a better model.
There's a tension between full capitalism, which often becomes inefficient because entrenched interests prioritize persistence of the institution over fulfillment of the institution's mission, and full competition, which often becomes inefficient because it cannot generate the institutional knowledge needed to run things efficiently. Bureaucracy and mature big companies are on the former side of the scale, bullshit startups and "artisan" (read: overpriced and poor quality) small businesses on the latter.
My ideal social system would make this tension explicit and create automatic mechanisms to break up large institutions and re-form them out of the skilled individual contributors at the bottom. Something like the California labor laws, where you cannot enforce non-compete agreements and it's very difficult to prove that the startup which just spun off stole your trade secrets. Probably even moreso, and applied to the government itself, as CA business climate has recently become relatively hostile to startups as well.
There's an opposing side to this dichotomy though: embrace competition. American democracy, with its separation of powers, is an example of this. The founding fathers explicitly set the government at odds with itself, because when "ambition is made to counteract ambition", the ambitious are so busy fighting each other that ordinary businessmen and citizens can go about their business relatively unmolested.
To answer your question: I'd absolutely work for an anarcho-tyrannist firm where I have no idea who the CEO is and managers can fire me on a moments whim, as long as I can walk into another firm tomorrow and get a new job. Job loss is only traumatic if all your eggs are in that one basket; if there's always another job waiting for you, just go get fired and take it.