I haven't seen the film; however, I have read the plot summary on Wikipedia. I am assuming the plot summary is accurate.
I think that our contemporary developed world cities are not conducive to the story told in this film. If a major city is experiencing a severe disturbance, such as a riot, the national government will send in military units to quell the disturbance. We have seen this multiple times in our country's history, most recently being the Los Angeles riots in 1992. I don't know of any incident in our country's history in which Special Forces are sent in to restore order. I could be wrong, and, if so, can someone name at least one incident?
A situation in which a modern city's government could be overthrown and the rabble seize control would be in a developing country, such as those in Africa and Asia.
I think if Christopher Nolan wanted to depict the United States losing control of one of its major cities he should have started in the first movie, and build it from there. The director could have depicted the decay of a great nation set in the near to far future with Batman being seen as the symbol of order over the chaos. The director could have introduced a military leader siding against Batman, and this military leader rallying soldiers who have defected to his cause. From there, it could have depicted the people rallying behind Batman and overthrowing the leader. I think there are approaches that could be tested to introduce the classic villains into this setting, and make it believable. This is not inconceivable - it has happened before.
I expect people to tell me that this film is based in alternate reality; however, one of the purposes stated by Christopher Nolan is to depict Batman in a realistic setting. The setting for this third film is not realistic. It is preposterous.
When all is said and done it's still just fiction. It will not ring true in a lot of details. Nolan tells this story in broad strokes and more than a few elements are simplified to get on with the story and make it pretty easy for practically anyone to get. That isn't to say it couldn't have been more nuanced (it certainly could), but it works sufficiently to tell the story he wants to tell.
One of the points I got out of this is that it's not really about just one city. To me Gotham represents America and western civilization as a whole. And any man can be Batman even if they're just trying to comfort a child in pain. And a lot of the stuff spewed by Ras al Gul, Bane and Talia is familiar terrorist speak.