It should also be noted that housing is super local. Building a bunch of new supply in the mid-west isn't going to lower the prices along the southeast coast. And for a less extreme case, adding a new house across town from me isn't likely to impact my house's price at all.
What would impact pricing is if people left an area (look at the 1 euro houses in Italy in towns where everyone has left). The mass migration to the US coasts and south doesn't seem like it's stopping anytime soon which will continue to put pressure on the local housing supplies.
I think that premise assumes that residents never move from areas with lower housing supply to areas with higher housing supply. A behavior rooted in economic gradients.
Migration in response to price differentials, voting with your feet, spatial arbitrage, spatial equilibrium, geographic mobility of labor, the Tiebout model...the phenomenon goes by many names.
What would impact pricing is if people left an area (look at the 1 euro houses in Italy in towns where everyone has left). The mass migration to the US coasts and south doesn't seem like it's stopping anytime soon which will continue to put pressure on the local housing supplies.