In a perfect world sure, government is fully funded and runs smoothly people care about the everyone etc.. etc..
But in reality I really would be very hesitant to want to live in that world. It is very scary to have a single organization control all your housing. At least with the way it currently is if you don't like your landlord you can go somewhere else. If the government owns everything your kind of stuck dealing with the same organization no matter where you go. Governments are not immune to corruption and can screw you over even worse in some cases then an organization.
In my opinion the best solution is many private citizens and small rental companies combined with government enforcing laws protecting both parties. However one big issues I am seeing is huge companies buy up everything in a small area and build a monopolies on rentals. That isn't good either.