For your housing example, we just need to produce more housing - but so many people are opposed to it. It's not that the private sector doesn't want to, obviously, they just aren't allowed to. You're making a good argument that we should allow for more housing to be built, but I don't see from your argument why it's better for that to be the government.

I can't think of many examples where the government does a better job producing things than the private sector. Even in countries with, for example, socialized medicine, and assuming you think that works well, the services (I think) are still provided by private companies. Maybe the VA Hospitals in the US - though I'm not sure that's an example of the government doing better or not.