>Manhattan is not a sprawl and a very desirable place to live, with super high rents to boot. Hong Kong, Seoul, Shanghai, and even Tokyo are the same, so I'm not sure what you are trying to claim here.

Those cities are actually impossible to have in America (yes, including Manhattan), because of zoning laws and various other laws. Manhattan is only allowed to exist because it's grandfathered in and the local laws allow it. Such a city could never be built anywhere else in the US without some huge changes in legislation (not to mention local culture, since that drives the local legislation).

>IF you want to solve your housing emergency, limit growth in some way

Tokyo works because growth isn't limited: it's very easy to build here, unlike in the US. Tokyo builds hundreds of thousands of new housing units every single year, while the US struggles to build any. This is entirely because of regulations.