As others have said, states do build housing. The real question is “why don’t they build more of it (let alone enough)”. The short answer here is that any not-for-profit housing costs upwards of two or three times what it costs to build for-profit housing. That’s for a variety of factors but mostly because the developments are expected to lose money on the back end so all of the developers have to make their money up front.

And then you have to factor in the costs of on-going maintenance; which, as anyone who’s ever driven on RI roads can attest to, states are uniquely bad at doing.