>It's hard to imagine some state law that prohibits a town (or neighborhood for that matter) from building out some kind of internet access.

That seems more like a failure of imagination, since ALEC[0] has been writing bills for state legislators to do just that for many years.

cf. https://www.prwatch.org/news/2014/02/12385/how-alec-helps-bi...

[0] https://en.wikipedia.org/wiki/American_Legislative_Exchange_...