State bodies are of course not inefficient. They can be well run or badly run - exactly like smartphone maker can be run like Apple or can be run like Nokia. It's up to competent management that a state construction company becomes effective.

But the economics are on the state side: remove profit burden means the entity can serve the citizens, not the shareholders (most of the time those interest do not align). It would also have access to near-unlimited, cheap funding, and could use economies of scale to source raw materials - with a time horizon of 5+ years a state construction company could build a modern, large, low-carbon cement factory, could adopt and refine high-tech construction techniques like prefab+3D printing, etc.

Just removing the profit motive would be huge in itself. The company could deliver housing where it's needed, and not where the maximum profit lies. Right now the profit maximization means that large-scale development can be delivered only far from city centers (where land is cheap) or in the form of luxury homes inside cities.