So if they are serviced by a public road at a huge loss to the state
They're not serviced by a public road. You might have a public road (really, a dirt track with the odd and rare sign) and then 20 house each 100 miles away from that road in different directions. So you'd need to string a couple thousand miles of fiber along the "public road", and then another couple thousand miles just to get those 20 houses hooked up. Multiply that a thousand times more and there you go.
Imagine wiring up a thousand small towns where each town is so spread out you need a thousand miles of fiber just to hook them up to the main line, which itself is tens of thousands of miles long. Then you can start to see the scale.