Sure building more housing, pushing prices down might induce more demand, but there are a dozen other factors (not in the control of the city) that also influence demand - job vacancies, crime levels, quality of schools, etc, etc.
The demand was there, the cost was just too high to satisfy it.
As a counterpoint, look at all the empty cities China built in the middle of nowhere. According to the "induced demand" hypothesis, people should have materialized to occupy them, but that didn't happen.
Cities currently prevent the market from meeting even the regular demand, let alone any induced demand. Housing isn't going to get cheaper by not building housing.
https://www.reddit.com/r/gifs/comments/4nkkq7/apartment_buil...