If American population was equalized across these other cities, there would be less pressure on the few hot places everyone wants to move now, since our population isn't growing so much these days.
> Eventually you run out of built out sprawl.
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. Out of all those, only Tokyo does well, but that wasn't the case in the 80s and is on the basis of a moribund economy and a not growing national population (one wonders when Seoul and SH will follow). IF you want to solve your housing emergency, limit growth in some way (or at least, make sure residents don't have as much money to bid up housing).
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.
Title = How Tokyo built its way to abundant housing
TL;DR: Since 1995 (yes, during the lost decade) they are building ~150k new "dwellings" per year. Wow.
This is a myth in central Tokyo.
Japan's economy is growing again (Nikkei is now at the level it was in 1990) and Tokyo's population has always been growing.
…but the rent isn't, because they allow infill development.
That isn't true though. Our housing emergency is limited to places that are growing and thriving. There isn't a housing emergency in Detroit or much of the midwest for example, just not many are thrilled about moving to those places (or want to leave them as soon as possible).