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.
Your sources contradict themselves. For instance, the Furman Center article states that adding luxury housing does not make housing more affordable. The paper from Northwestern states the opposite (luxury housing decreases surrounding rents). Just from looking at the paper from Northwestern, their area of study has significantly lower rents than their control group. It’s not as clear cut as you make it seem. Also, jobs growing with housing supply could possibly be an example of induced demand.