> Justifying the tax to provide a service with an existing private provider
I think you misunderstood. The tax would be on the private provider (serving profitable areas) and for the benefit of the public provider (serving unprofitable areas).
> If the city service tried to operate city wide, the private company would sue them claiming they can't compete.
The idea of taxation instead of monopoly power is not having the city operate anywhere a private operator would, in the first place.
The argument is that using monopoly power distorts the market to such an extent that it leads to gross inefficiencies and that more overall value can be extracted through competition and taxaction.
> The company may sue even if the city is only trying to extend service to the underserved for the same reason.
That part I don't follow.
Firstly, the notion that lawsuit against an entity that could legislatively preclude one is possible, is questionable at best. We are, after all, discussing, their existing use of monopoly power.
Secondly, even considering suit as a metaphor for seeking any kind of recourse (other than lobbying for not getting taxed at all), why would they want to?
> Some of these success stories are more luck then repeatable solutions.
I assume by "luck" you mean that the eventual circumstances were unforeseen by the original architects of the solution. I admit that I can conceive of a situation where that's at least theoretically possible (unexpected growth "in town" creating enough profitable customers to support an otherwise failing teclo), but I'd say the burden is on you to show that "some" isn't vanishingly few or even zero.