This article is completely orthogonal. Yes, building more pushes price down. Eventually though, you stop being able to increase density economically, and at that point the only way to prevent housing prices from increasing is rent restrictions.
It's important to note that even according to your article, you need to drastically increase supply even for a modest decrease in rent.
No one here is against increasing density. It is however insane to believe that increasing density is enough to fix the problem. Cities at the edge of density still have affordability issues, whereas much less dense cities with appropriate rent restrictions don't.
There is not a single reference to induced demand here. As long as housing stays a profitable investment, and as long as density cannot be increased infinitely without increasing marginal costs, then rent will rise.
The only long term solution is to reduce the profitability of speculation on land prices, so that only productive activities, such as building, are profitable. Rent restrictions are part of this, as rent is a large part of the profitability of land.
And rent restrictions can work. There are many cases where they have been implemented without a significantly negative impact to mobility. So why oppose them?
