HereForTheBeer: Brings up the question of how much of an obstacle the city itself is presenting to the problem. Broadband requires running lines and - as Verizon asserts - gaining access to buildings to make connections, and if the city isn't facilitating that process...
The whole point is that Verizon in particular and telcoms in general got shitton of money not only in federal grants for last-mile rollout, but New York (both State and City) also offered substantial tax breaks and other goodies for them to do the job.
Back around 2005 or so. The money was pocketed, bare minimum of effort was shown (hence
the recent lawsuit against Verizon for failing to roll out FIOS as they were supposed to - Verizon in particular got a sweet, sweet deal out of the "investment" money from taxpayers that they used to stuff own pocket with).
The only thing New York could do is attempt to break down the mono- and duo-polies (old Time Warner and Verizon actually "traded" areas with rumored non-competing verbal agreements to make sure people have no bloody say in what they get), but aside from the red part of New York State going bonkers about government interference, current federal setup does not exactly inspire confidence.
Not to mention that all the representatives get serious money from telcos in the first place.
There is a reason that the US, a country that "invented" the internet, is already long behind on quality of service and just basic speeds compared to other countries, even in the largest cities (to avoid the "oh noes we took money to deliver internets to the bunnies but it actually costs so we'll just wringle our hands and pretend we did not already get paid to do the fucking job in the first place" arguments straight from telco PR playbook).
Also, if you read up on other cities trying to set up municipal fiber and sell its use to any company willing to provide service, you'll immediate run into lawsuits from the usual suspects claiming government interference in the Holy Free Market™ and often winning by sheer capacity to out-spend local authorities on court costs.