I disagree. Cities are in a endless race to build more housing. They need to continue building housing to keep prices temporarily lower, a metaphorical treadmill as more people will always move into the city. If a city stop building housing, prices will go up for sure because demand continues to increase. Cities of course always have more demand, but that is their nature as economic and cultural hubs, we have no choice but to try and match this demand.

Housing prices will not be low without building more housing, except your city has a specific reason that lowers demand, like lawlessness, economic ruin or some other disaster.