[AnthonyMouse]

> "Or rather, the fewer poor people around tends to mean rich people find it even more desirable."

But why is that a problem? It's like complaining about free money appearing out of thin air. If every rich person in the entire world wants to move to your city, that's really good. It would be a wonderful tax base. And there are a countably finite number of rich people, so there comes a point when you have literally every last one of them.

Having to build enough housing for every rich person in the world is ridiculous, but the reason it's ridiculous isn't that you couldn't physically do it (if there are a hundred million rich people, that's only a single digit factor more people than live in Beijing or Shanghai). It's that they would never all move to one place like that -- especially because every other city would be competing to keep them.

And if density is actually such a wealth magnet then every city should do it. Then the outflows and inflows would net balance and there would be no net migration of rich people to any city in particular. If you somehow got more than someplace else, what are you complaining about? Build even more housing to see if you can get some more, then go spend their money on your roads and schools.