I mean... The very existence of wealthy cities is a sort of proof. Remember that for America to temporarily be one of the few examples where dense cities were less wealthy than spread-out suburbs and exurbs, we had to combine massive subsidies and financing with good old-fashioned racism.

What I don't agree with from GP is the idea of real increases in housing costs for those already in cities. The rising tide lifts most boats, if density isn't being unduly suppressed. So, density increases housing value but also the wealth of city-dwellers, relative to everyone else. Supply keeps up with demand, except where we won't let it.

>the increase in demand comes from having, presumable, more amenities

Not necessarily. It can also come from the increased opportunity for exposure to people and culture.