From what I've seen, a lot of people on the economic left actually agree with those criticisms of rent control, and would much prefer to see true public housing

From what I've seen, a lot of people on the economic left actually agree with those criticisms of rent control, and would much prefer to see true public housing take that place. Non profit NGOs don't typically have the capital to own the relevant land and buildings. And when they do, they typically see it as better use of that capital to sell it or rent it out at market rates and use that liquid capital more directly in whatever their mission is. It's typically only .gov that has the right means, motive, and opportunity to pull off public housing in the face of the rest of the market. At that point, when there's no .gov impetus behind such a thing, rent control is viewed as the least shitty of a group of shitty options.