I believe the goal is not exactly cut off the city completely, it is to reduce the flow of goods to and from the city, to the point where the current status quo collapses.
While reducing the flow to zero is ideal, reducing the flow to the point where stocks are consumed faster than they are replenished means that the city will find themselves without adequate food supplies soon. Big cities like NYC require large and well-organized streams of food and goods to function; even a relatively small hiccup in that stream will have a noticeable negative effect on the city, especially if they have no time to prepare...
I believe the goal is not exactly cut off the city completely, it is to reduce the flow of goods to and from the city, to the point where the current status quo collapses.
While reducing the flow to zero is ideal, reducing the flow to the point where stocks are consumed faster than they are replenished means that the city will find themselves without adequate food supplies soon. Big cities like NYC require large and well-organized streams of food and goods to function; even a relatively small hiccup in that stream will have a noticeable negative effect on the city, especially if they have no time to prepare...