What do you mean it's not a supply problem? Suburbs and the housing within them aren't naturally occurring features with limited supply. They're not oil deposits. You can just build more of them.
Same thing with places like NYC or Paris or London. The point isn't that they need more development, it's that other places need more development so people who want the NYC experience in the US don't have exactly one city to choose from. You don't make NYC cheaper with more building in NYC, you make NYC cheaper by making more NYC like cities.