Hells yeah. That's why one of the ideas above was that the government should be a significant force in housing. Part of that might be buying up existing homes, but a lot would be funding the construction of new homes.
I didn't mention it above because while related, I considered it out of scope for that comment. But I'm also a fierce advocate for abolishing low-density zoning entirely. What my city calls "LMR" (low-medium residential) should be the bare minimum zone for residential areas. That still permits single-family separated homes to be built, but it also automatically permits 2–3 storey townhouses and apartments. Plus zoning areas near (say, within a 400 m walk of) train stations for medium-density residential. (All mixed-use, of course.)