The high cost of housing is simply cause by the market failure or market inefficiency of zoning density restrictions which benefits landlords/land holders over the renters and those who wish to buy housing. Prices are higher because of scarcity and the scarcity is politically induced called "rent seeking". This rent seeking was first explained by David Ricardo regarding the "Corn Laws" which were a tax on imported grain causing workers to pay more for food/bread. Farmers received more money for their grain, but the landholders of the land the famers used simply charged higher prices.

Fix the market failure and free markets will create more housing. Renters will pay less for housing, there will be less commuting which causes less pollution. There will be more disposable income which can be used to pay for goods and services thus stimulating the economy and employing more people.