This is absolutely wrong. Pretty much every single piece of evidence we have shows that zoning has a massively impactful effect on the supply of housing. Similarly, the vast majority of studies looking at the issue show that induced demand doesn't occur for housing (that is, adding housing supply does lower prices, rather than simply causing people to consume more).

With regard to NYC, even though it has added around 250-300K housing units over the past fifteen years or so, it has added around three times that in jobs. If housing supply isn't increasing in line with people, you will see increases in prices.

Some links:

- https://www.planetizen.com/news/2019/06/104783-doubt-cast-in...

- https://www.youtube.com/watch?v=c7FB_xI-U6w

- https://furmancenter.org/thestoop/entry/supply-skepticism-ho...

- https://furmancenter.org/files/sotc/SOC_2017_FOCUS_Changes_i... (the key quote here being: "In 2016, NYC had 8.2 percent more housing units, 11 percent more adults, and 16.5 percent more jobs than it did in 2000.")