Yep. Exactly. With the caveat: the increase happens by increasing the _density_.
> Seems like that turns standard econ on its head, so can you help me understand who you reached that conclusion?
Here's another example. Suppose you give a billion dollars to everyone. Will everyone just become rich?
Housing is similar. When you build denser housing, it increases the attractiveness of the area for employers. They get access to a larger labor pool, so companies near dense housing are long-term more competitive.
This in turn increases the housing price, as workers want to live closer to employers.
Rinse, wash, repeat.
The end result: no large city managed to lower down housing costs by increasing density. It's a simple verifiable fact.
Edit: I checked data for Western Europe, Russia, US, Japan. It's possible that some citi in India or Malaysia managed to do that. But I don't have data for them.