The reason new construction never works like this is because developers only build housing when there's already a severe shortage of housing in the metro area. They respond to price signals, and the price only starts going up when you have multiple bidders bidding for the same home. And why wouldn't they? If they built housing in places that already had an abundance of housing, they're making an economically foolish choice and will go bankrupt. When you observe that developers never build affordable housing, you're observing the effect of selection bias: in a region where there are enough houses for everyone and hence they're affordable to the average worker, developers aren't going to build even more new houses.
You can observe this throughout the Rust Belt: there are more homes than people, so prices are very affordable, but developers would need to be insane to build even more houses (outside of specific neighborhoods or suburbs that are locally hot). Also when you get a macroeconomic crash in the middle of a housing boom: the houses get completed, they sell for dimes on the dollar, but nobody has jobs anymore so they can't afford to buy them,
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).