The biggest problem that increasing housing supply can solve is the gap between minimum and median apartment price. In places with very constrained housing markets the cheapest slumlord apartments are very expensive (~70-80%) compared to the price of well maintained apartments. Increasing housing supply doesn't do much to the median housing price (since new houses are expensive), but it lets the price of shitty apartments drop a ton.
Building adequate housing also brings down the medium cost, by a lot. At worst, it prevents the median house from rising in price.
Prices are set through a combination of supply-demand and cost of providing housing. Almost all increase in housing costs are coming from land price increase, due to land shortage from planning policies that limit land use density.
Housing has been made into an investment first, and a home second, by creating housing austerity and shortage. The only way to prevent housing from being an investment is to stop the artificial shortage of housing.
This is the problem - not that a brand new McMansion is going for 3,000 square and $900k - it's that the 750 crackshack is going for $500k.