This seems far more complex, as there doesn't seem to be a natural way to deduce how the faces are connected. By always sorting the intra-face coordinates last you hide the information in which of the 4 dimensions the face really extends, and need to code that information in an unnatural way in the face code. Tracing an orthogonal or diagonal becomes really easy in the natural coordinates.
This seems far more complex, as there doesn't seem to be a natural way to deduce how the faces are connected. By always sorting the intra-face coordinates last you hide the information in which of the 4 dimensions the face really extends, and need to code that information in an unnatural way in the face code. Tracing an orthogonal or diagonal becomes really easy in the natural coordinates.