> Many people want to live in the former, but must settle for the latter, due to lack of affordable NYC housing.
That's because they _have_ to work in NYC. Polls show that something like 80-85% of people in the US would prefer to live in suburbs.
> Then look at the price of housing in say, Cheyenne, Wyoming: Even cheaper, because people want to live there even less.
Well, yes. Land is not scarce in Cheyenne, so housing is cheap. But people don't flock there because they don't have any job prospects in WY. See my notes about remote work.
> Or look at your own example: People want to live in Tokyo more than they want to live 3-4 hours outside of Tokyo, hence the pricing for the latter is lower.
How about: "People HAVE to live in Tokyo, because there are no job prospects outside of Tokyo"?
> In my experience, most people in the US want lots of square footage within the city, and either settle for suburbia to get the square footage they want, or settle for less square footage to get the city living they want. This goes for both renters and buyers.
Well, sure. I would love to live in a mansion with a private lake, in the middle of Union Square.
> How, then, would increasing the price of in-city housing (by reducing the supply, by replacing denser housing with less-dense housing) allow them to realize their big-city-big-living desires?
You assume that people _want_ to live in big cities. People want to have access to big city amenities, but not necessarily live there all the time.
That's why suburbs are such a desirable place. Think about this: what if you live 1 hour away from the city core? This still allows you to easily enjoy all the amenities like theaters and shows. Or to periodically go to your favorite ethnic restaraunt. But it's _way_ too far for daily commutes so it's impractical.