It's not even that though. Looks like public utilities are only offered in areas where those utilities are cheap to provide or abundant, and private utilities fill in a gap in harder to reach areas.

The study even points this out as a foot-note but then focuses on rate of price increase versus nominal price. It should not come as a surprise that in areas where utilities are less abundant the price will increase faster than in areas where that same utility is plentiful.

That’s roughly the opposite of the development of electric utilities in the US. The IOUs owned dense urban areas and refused to electrify further out. It was only the rise of public municipal utilities that got them to go to the states, implement the regulatory compact, be granted rate of return, etc., and then they began building out more.