https://www.6sqft.com/nearly-250000-nyc-rental-apartments-si...
https://www.nytimes.com/2018/03/16/realestate/brooklyn-devel...
If there weren't luxury multi-million dollar apartments to buy, they'd be buying the brownstones anyways. And given that the multimillion dollar units sit on the market far longer than the more affordable housing stock, is there even really high demand among the wealthy to own premium housing?
Luxury housing gets built because it's the only thing that's profitable to the builder once you take into account zoning and permits and regulations that need to be satisfied in order to build. What we really need is relaxed policy that allows for the profitable building of run-of-the-mill, average housing.
Poor or average people buy a house in order to save money on rent. Rich people don't care about that amount and can easily get their stuff moved with company money. They recover the rent vs mortgage cost via increased flexibility.
There are a few areas that were designed as slums from the beginning: Lower East Side in Manhattan, parts of the West Side in Chicago.
Taking Silicon Valley, if 25,000 high end apartments were built, that would take a lot of pressure off low end, because well paid people wouldn't be taking them out of desperation.
Short answer, yes. If you're interested in detailed information about NYC housing, I definitely recommend checking out the Housing and Vacancy survey data (https://www1.nyc.gov/assets/hpd/downloads/pdf/about/2017-hvs...)
https://ny.curbed.com/2018/4/12/17227574/new-york-rent-marke...
Building more housing, and giving incentives to build as much housing as possible is indeed a complete solution.
They have something like 65 MILLION excess, unused apartments, almost exclusively targeting the luxury market (because they are created and valued as investment first, housing second), and they still have extreme affordability issues.
Building more housing is absolutely not a complete solution.
Housing isn't just about the number of houses in a given country. It's about having available housing where the demand is growing.