Yes, as it would be a public good to everyone to be able to know where the potholes(that aren't profitable to fix for these private companies apparently) are

Yes, as it would be a public good to everyone to be able to know where the potholes(that aren't profitable to fix for these private companies apparently) are so they can avoid them. They might take a step back and realize that it would be more cost-effective to just own the roads, in which case your thought experiment ends where we are, because where we are was a place reasoned to(to an extent).