Interesting. I was unaware of the state of telcos in NZ. I found this wikipedia article to have some additional content: https://en.wikipedia.org/wiki/Telecommunications_in_New_Zeal...

Using only that article as a resource (lazy, sorry), it seems that the telco infrastructure improved because of competition. It doesn't really seem to be a private/public issue, but that multiple companies got into the action.

All of Iceland's infrastructure was sold off in one huge chunk, forming a private monopoly. This may become a decent test case for whether government-operation or private-operation makes a difference. (In contrast to the wiki article, which suggests that competition is the thing that matters.) Like the grandparent comment, I expect very little from the private operation of Iceland's telco infrastructure, but I'd love to be surprised.