With a greater supply the clearing price will be lower. That's a trivial statement.
The real problem is elsewhere - by constraining supply landowners are inhibiting economic development. Newcomers have a choice, if accommodation is too high they'll go elsewhere, so economic growth in productive industries will take place elsewhere.
Man, not too long ago I shitcanned a new job 4 days in over the insane housing prices. A good number of my colleagues had a sideline in Airbnb, that asset inflation machine.
There's far too much capital sunk in real estate, where it could not be more unproductive.