The idea of what a public utility is, economically, rather than just legally is not a new point of discussion. Philosophers like John Stuart Mill argued for the public provision of water and gas, based on them being natural monopolies (see here, V.11.36).
Public utilities are a type of public good provision related to services that may have a tendency to form a natural monopoly. Natural monopolies are cases where it may be more efficient to have one provider rather than competing providers for a service, due to large economies of scale, large barriers to entry, inelastic demand of consumers, the need for over-engineering (being able to provide for peak demands), among other factors. Providing tap water, gas, or electricity, usually requires a lot of infrastructure that is expensive to put into place, so this is one example of why these goods do not have a lot of competition in their provision, as these goods tend to exhibit naturally monopolistic tendencies.
Although the internet requires a large infrastructure and may have large economies of scale, it does not seem to neatly fit the idea of a public good. A public good is usually non-rivalrous and non-excludable, but the internet however seems to definitely be excludable, and in some places, rivalrous, at least partially (sharing bandwidth with your extended family and/or your neighbor who downloads a lot of mysterious content). There is also a laymen argument to be made that the internet could be a luxury good instead of a necessity, making it inappropriate to regulate as a public utility.
There is some evidence that monopolies or oligopolistic competition in related industries, such as cable television, decrease the quality of its provision in the absence of regulation, but my concern is not to debate regulation with this question.
My question is, what economic literature is there for characterizing the economic properties of the internet, either as a public utility as opposed to a luxury or something else?
In discussing the answer to this question, papers regarding whether the internet should be regulated as a public utility may pop up, and that is okay. But the primary question I have is not what the nature of regulation should be, if any.