Government can build if private industry will not. If you argue "we can only fix this with the private sector and private investment", welp, we tried that and we're plain ol' fucked at the moment.
Define we. My example shows government housing can be done. Swap out people and policy if needed. "Insanity is doing the same thing over and over again and expecting different results." -- Einstein
Vienna is a great example.
https://www.youtube.com/watch?v=41VJudBdYXY (Youtube: Vienna's Radical Idea? Affordable Housing For All)
https://www.youtube.com/watch?v=d6DBKoWbtjE (Youtube: Does Vienna Have the World's Best Council Housing?)