You are partially right that Econ-101 doesn't explain it well, but if you take Econ-201 it does explain how housing supply/demand works. Why it doesn't work as easy as 101 is that the location matters for the 'good' unlike say cars which can be shipped in from anywhere. And also zoning artificially constrains land from being used for housing.
NYC on the other hand is a good example of what you’re talking about - it’s expensive to live there and pretty dense already. But Tokyo for example had 150k housing starts on a recent year, which is more than LA, NYC, Boston, and Houston combined (source: https://www.google.com/amp/s/www.wsj.com/amp/articles/what-h...) - amp link to get around paywall.
I think there’s tons of evidence that we just don’t build enough myself. In bangkok, another market, they’re throwing up more new tall buildings every year than almost the entire USA does.
The Midwest and the South are both way ahead of California on the whole "just build more housing" thing, for example, and have been for many years. And yeah, it makes us somewhat cheaper than a coastal city if you have California dollars to burn. But our Price-to-Income-Ratio's are still in the high 5-7+ range too, just like everywhere else.
We have basically zero population growth, and every single stray piece of land is getting built on right now (record high construction, record high new housing starts, for the past three years straight) and housing prices still rise 10% to 15% every single year like clockwork, with no end in sight.
"Just build more" sounds really pretty, but that alone will never get housing prices back down to a real-world-affordable figure for most people.