An extremely provocative essay by Greg Rehmke. Incidentally, I've known his name for a few years now, but just met him at the APEE conference. I think his work warrants more attention from free market fans than it has thus far received.
I didn't read this whole essay word-for-word, but I think the one major stumbling block is that densely populated cities such as New York and Hong Kong rely on imports of food etc. So it's a bit too flippant just to say, "If NYC can have that density, so can the rest of the world!" But as I say, maybe Greg deals with that objection and I just didn't see it.
Generally, I am aghast when people say things like, "Our Earth can't support so many people," and when even free market types like Tyler Cowen lecture us on the number of our children being the biggest determinant of our "carbon footprint." Next time you are in a plane, just pay attention to how much empty space you fly over. Then realize that the Earth is 70% covered with water.
Once humans figure out how to profitably build floating colonies, the Earth could easily support one quadrillion people. And in terms of us using natural resources? We have quite literally only scratched the surface of the material wealth in this oblong spheroid.