If I had to guess it's not so much the actual cost of building the house as it is the profit margin of those who are building homes. Why build a $200,000 "starter home" when you can build a $478,000 home with gigantic margin on "luxury" trim like cheap granite countertops and "hardwood" floors for roughly the same cost? And then once you get the ugly design down you can just copy and paste it with few adjustments and save even more money.

Unfortunately we have bad incentives aligned here versus stated goals.

Manhattan and San Francisco are like Japan and Argentina in economics. They're just not the same market as most places. In Manhattan in particular the value really is the land.