The very notion of a center of X makes a lot of sense when such a simplification is useful. For mass, the center of mass is a lossless (or nearly so) simplification. In physics, the movement of complex object can be understood with only its center of mass.
Not so with economics; I'm very skeptical of a "center of economic activity" constructed as shown in figure 2. What questions does it answer well that a proper geographic distribution does not? (It certainly doesn't imply that all economic transactions go through that "center".) I think it misleads more than it helps. (And I'm not even going into the 3D -> 2D problems.)
Perhaps centre of a graph is more useful - economic activity is almost always an edge between two nodes, so the usefulness of graph theory seems apt (and afaik common) with economics - so a map showing the volume / value of transactions between actors would perhaps be useful - I have not seen all the maps here but it would presumably see NYC glowing with shipping and financial nodes ...
The center itself is not important. The point is to show an evolution through time. Geographic distribution are clearer and more precise but only handy for a given instant.
Not so with economics; I'm very skeptical of a "center of economic activity" constructed as shown in figure 2. What questions does it answer well that a proper geographic distribution does not? (It certainly doesn't imply that all economic transactions go through that "center".) I think it misleads more than it helps. (And I'm not even going into the 3D -> 2D problems.)