Ok, I will try to explain this a simple as I can in order to keep it short.
The cable and telcos have to offer service to unprofitable areas as well as the profitable areas and charge the same rates for both. This is part of their ability to have a monopoly in the area. Now, in some areas, there is competition but not because the infrastructure was duplicated but because they had to lease it to the competition at costs of operating it and also serve those not profitable areas.
So a municipality steps up and uses tax dollars to build out new infrastructure that competes with these other setups. They then go into direct competition with them and suck up the profitable areas leaving the cable and telcos with only the unprofitable areas and a few stragglers in the profitable areas.
The end result is, or could very well be, that not enough profit is left available for the telcos and cable companies to do upgrades in those areas. And before you think they are rich companies over flowing with cash, first, they typically segregate their areas of operations where time warner of Atlanta might be a different company from time warner of Columbus Ohio but owned by a parent company. Each area would be separate as far as financials go. Second, if their cash cows disappear, they will likely no longer be overflowing with cash.
Also the municipal only doing the infrastructure is not really what is being considered here. What is being considered is the municipality selling off their excess bandwidth and purchasing more in order to go into direct competition with the cable and telcos. Some of the plans I have seen deliver the product free of monthly charge and is based on taxes paid. This is like the cable and telcos being able to charge each and every citizen of an area whether they have the service or not.
But I like your idea of the municipality owning and providing infrastructure that others lease until another recession hits and they neglect it because revenue is down or some loon gets elected mayor and decides to divert the funding for it to something else he things is more important like flags and colored lights lining the main street going through town or a brick crosswalk on one of the busiest intersections that has regular truck traffic (Yes, both have happened in my town- had to put a levee on the ballot in order to fix potholes because they spent that money on other shit) in order to enhance curb appeal.