Earlier quoted context omitted.
Because government has a unique pricing advantage, they get additional value from the houses they build in the form of all the positive externalities and property tax revenue. So projects that wouldn't be profitable for private builders might still be worth it to the government. So it should be both. They're just gonna pay builders a sum anyway so it's not like they need to shoulder the full upfront cost anyway.
Do you have example of another area the government has higher profit margins than private industry? I can't. And if I was going to think a government would build housing, it would be in places that are cheap and I could mass house a bunch of people, not in hip expensive cities which is what people want when they talk about this. But surely soviet style huge blocks of tiny t0 apartments all stuck together is a dream..…
Public transit. Capturing enough money from fares is difficult, maybe impossible, but it's quite profitable if you can capture the value generated by the enabled economic activity and raised property values.
The same really goes for most infrastructure. There's a reason the government operates nearly all the roads. Also the fire departments and police stations