Earlier quoted context omitted.
Housing prices are not driven by scarcity, they are driven by financialization of our economy. There are multiple cities in England where population has decreased but house prices increased. During lockdown 700k people left London, but house prices kept going up.
Triple the housing supply. Prices will go down.
"Just building more" alone isn't ever going to lower prices enough to make housing affordable for most, no matter how many more units you build.
You have to decommoditize housing, or stop force-preventing natural depreciation, or at least put ownership caps on it, or some other thing in addition to the construction.