New market rate housing gives wealthier people something to buy so they stop bidding up the price of older homes. This immediately relieves price pressure on the older housing stock.

Leftist dreams of a government funded social housing utopia in the United States and the UK are just that: dreams. Reforming zoning on the other hand will strongly encourage developers to quickly add higher density housing in job rich urban areas.

House prices are supply and demand. More units, lower price. Imagine 1000 homebuyers for 950 houses. Capitalism says the houses go to the top bidders. Communists might use social credit or something. Technocrats might score on IQ. But there is no system that could possibly result in fewer than 50 people being homeless.