In SF, NYC (where I live) and other US localities, the issue is not family income but rather is the use of politics to limit zoning density and thus artificially creating housing scarcity.
Thus, renters pay more than they otherwise would with an efficient market and billionaire land-owners have much greater wealth than they would in an efficient market.
In NYC, we had a somewhat similar situation with Taxis. Medallions were artificially limited to 13,000 in this city of 8 million where many people do not own cars and use mass transit and taxis. As a result of this 13,000 limit, taxi medallions had a market value of $1.2 million.
Then thankfully, Uber came along, thus creating a larger supply of hail-able taxis and the taxis medallions now have a market value of $700,000 or so and some taxis are no longer in use.
In NYC, our current mayor has two properties that he rents out for a total of $120,000 per year. He is able to get this high rent because of city laws that limit zoning density. Thus, he has every incentive to want to artificially limit zoning densities.
Thus, while many liberals fret over income-inequality, they still support zoning regulations in cities such as SF and NYC that amount to a transfer of wealth from lower income individuals to wealthy individuals.