Ii hate these cliffhanger endings.

What happened after the bomb is what happened after the bomb, but that's got nothing to do with whether NYC gets nuked or not. I agree the aftermath would make an interesting film in itself, but that wasn't the focus of the film. The story that Lumet was telling was about how a war could start by accident and ended with the nuking of NYC to prevent that war. It's the audience's job to ponder the hypothetical future consequences of the fictional story they've just witnessed. You claimed the ending was a "cliff-hanger", and I assumed you had mistaken the freeze frames for an inconclusive ending. The use of freeze frames was just a popular stylistic device at the time started by the French New Wave. Lumet used the freeze frames to highlight all the lives that would be suddenly cut short when the bomb detonated... that's it. I too have my doubts that the ending of the film would have occurred without a serious coup attempt, but that's a not what your original posting seemed to be calling into question.