Government already owns plenty of land, even in most large cities. If you can get a bunch 30+ story housing cheaply and quickly, you can make a dent in the housing problem. Look at what China is doing.
Not in Seattle. The city is having huge issues finding places to build low income housing. Whenever they do identify a location, a bunch of lawsuits show up from nearby residents. Sometimes those lawsuits go somewhere, and the city has to start planning all over again.