> Housing is literally exclusively a supply and demand problem. If you want rent to go down, allow more building

Wrong. Without Land Value Tax the housing market simply doesn't clear. If there is no force to make house and land owners to sell to those who would actually utilize it better, they will sit on it forever until a huge ass corp or gov eventually buys them out for ridiculous price. As an owner you just have to wait while not paying virtually anything. Everybody else who actually needs to live, work or produce something in that location has to rely on new housing in ever increasing urban sprawling cities.

San Francisco is a prime example of this and apparently always has been as Henry George showed more than a century ago.