I love that clip (and pretty much everything else in The West Wing).
But there is actually a reason the Mercator map (which distorts size) is so widely used, which isn't really mentioned in the clip.
EDIT: Actually it is mentioned in the clip! Treats me right to rely on memory :) I'm leaving the explanation here for anyone that hasn't seen the clip. Thanks yummyfajitas for pointing out my mistake.
The gist of the reasoning is this: take any 3D object, and try and map it onto a 2D surface, and you're going to have to distort something. In the case of the Mercator map, the plan was to make a map that clearly showed "shipping lanes", i.e. if you draw a straight line on the map from one point to another, you can travel in a straight line in the real word between those points. This is important for sea travel (the Mercator map was created in the 1500's). The trade-off to this decision was that sizes were distorted.
See also: http://en.wikipedia.org/wiki/Gall%E2%80%93Peters_projection