We could have non-profit businesses for any and every kind of activity. Of course they would have to be competitive. They would have to advertise and do PR. They might need lobbyists. They might need to form interest groups. They would need good product and package design, and to do market research, and all the other things that success in a tough business climate requires.
We should have non-profit agri-business, engineering, real estate development, IT, logistics, waste management, etc.