The first pitfall that I could see with these map projection is that its name, equidistant, gives the impression that the distance on the map is exactly proportional to the corresponding distances on the ground. This is not the case, and therefore it could be misleading. The equidistant conical projection is helpful because it is unique in the aspect of showing the world at an angle in which spatial relationships of the countries around the north pole are located.
One bad thing is that this north pole orientation causes severe misrelationships among countries around the south pole. The Plate Caree projection is a useful equidistant projection because it's rectangular shape makes use of the gridlines easy, and it is in the rectangular motif of common projections, but also, because of this, people might not recognize the significant parts that it shows.
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