Even if that is his vision, it won't work. You can't be king of a frontier for very long unless your rule is very competent, minimal, and low-cost. The tighter your grip, the more star systems will slip through your fingers.
Everybody likes to imply that Elon is going to make some sort of shit new society in space. Perhaps they'll get as far as trying, but the odds of it working out are questionable on social grounds alone.
In general, people living in hostile environments develop higher levels of trust and social responsibility. When you live closely with people, where everyone's choices impact everyone else, when a single person intentionally screwing things up could doom the entire community, you get societies that are pretty much the polar opposite of the archetypal billionaire libertarian vision.
Elon hasn't talked a lot about the social aspects of a Mars settlement. Maybe he doesn't care and figures that's up to the people who go there and his mission is just to get people there. Maybe he would agree with you and that's the point. Who knows.
I highly doubt he's naive enough to think the social outcome of a Mars settlement would be some standard issue Earthly political outcome or one that would exclusively favor him. If he is that naive he will be disappointed.
Even if that is his vision, it won't work. You can't be king of a frontier for very long unless your rule is very competent, minimal, and low-cost. The tighter your grip, the more star systems will slip through your fingers.