[postingawayonhn]

I don't think that's necessarily true.

Raw cost of housing is essentially the cost of the land + the cost of the building.

In established cites the cost of land is high and developers tend to build expensive buildings on that land. Low-income workers than move to older buildings as they're cheaper (expensive land, cheap building).

In a new greenfield city the land will be very cheap (for whoever established the city) so that can keep the cost of housing down (cheap land, expensive building).