Public housing is hardly a libertarian's dream, but even from a laissez-faire viewpoint this makes vastly more sense than rent control. If you want something,

Public housing is hardly a libertarian's dream, but even from a laissez-faire viewpoint this makes vastly more sense than rent control. If you want something, and the market isn't providing it, you subsidize the supply or you buy it directly. That might distort prices relative to an independent market, but if your public policy is stable they'll still reflect relative demand and supply. Subsidizing purchases or constraining prices doesn't just alter the market, it degrades the signal - and usually doesn't fulfill the goal except in the very short term.