The article mentions building limits. Call it "zoning" or "neighborhood preservation" or "green belts" but it's all State control over what should be private property decisions made by individuals. Artificially limiting supply through a restrictive building permitting process will drive up costs. Hence, the need for rent controls.
So the State controls both the supply and price of housing in these metro areas. Any public figure or pundit who blames "capitalists" or "failure of the free market" for the housing woes should be laughed out of the room.
How can we solve the problem? Stop trying to fix it with government. Allow rents to equalize at the market rate and allow supply to be determined by the market. Until the statists relinquish control, the problem will never be resolved. But the upside is that we will get to read these nice Economist articles forever.