Soooo.... private business is interested in areas where they can make slim to no profits because they can make money at it?
This is what you just said.
Ouch. See your chiropractor.
Also: in the realm of public works, plenty of poor people want running water and sewage treatment plants and, oh, rural electrification, but either they can't afford to band together to get infrastructure investment money or the private sector doesn't think it's worthwhile to serve such a small, spread-out population. So who steps in?