If the Internet were more mesh friendly this would make sense, but as long as you need to pipe all the data in a town through a backbone provider someone holds way too much power in the relationship. With power companies third parties can run their juice over lines that goes to homes without touching another plant. The state can maintain the switching stations, but otherwise power never needs to pass through another third party.
Or in a state like PA, you may never get power from your choice provider, because you get to pick your power company here. So I can buy from some business out of Erie who is only serving power locally while I get all my juice from another company, but state regulation says that I get metered billing from my service and not power provider.
That can't really work with the Internet. Fundamentally, if the state owned the wires and the switching stations, they would own all the infrastructure. There is no equivalent to power plants in IP - unless you want private switching stations, which means you are not emulating the electrical grid (usually). It is kind of brain dead simple for a municipality to provide a dumb wire and routing, though.
I think it is worth noting that where I live (a town in PA called Kutztown) the borough a decade ago started a township owned telecommunications business subsidized by taxpayers. It operates as a semi-private entity, and since the huge township investment (it is still paying off the 15 million investment) the data rates have never gone up once, and the pricing has only gotten worse - it started at 10 / 10 mbps for $25, and today the rates are 10 / 1 for $30 and 10 / 8 for $60. The company has no incentive to improve their infrastructure and bureaucracy guaranteed the deployment was hugely inefficient for taxpayers to foot the bill. The only benefit was that the traditional telecom giant in the region, Service Electric, dramatically slashed prices in the borough in response to the town sponsored option - but their service now stays just as expensive as HomeTown Utilicom, and neither improve service or reduce pricing because now it is just a duopoly where one only expands through taxpayer money and the other has more lucrative markets to leech dry where they are the only cable provider.
So what I am saying is that the public option may not be the sunshine and rainbows everyone dreams of. The state is dramatically inefficient at building anything. They will spend ten times the money and get a tenth the return because they have only tertiary cost pressure and massive bureaucratic bloat. The perfect scenario is where you can somehow get infrastructure at private enterprise prices (and that means you had to get a profit motivated cost deferring entity to initially deploy the infrastructure to keep the expenses low) while somehow having the state pay off the business, and then give away wire access to its constituents for free or cheap. And then you have to constantly figure out a way to apply market pressure to improve the infrastructure, rather than just stagnate on the first attempt.