To amplify Paco's response, the orthogonality of geodetic coordinate axes simplifies the Euclidean norm. Using an orthogonal system is equivalent to setting the angle(s), between principal axes, in the law of cosines to 90 degrees. That is, coefficient
F in the
metric tensor is zero when geodetic latitude is used instead of geocentric latitude, see equation 34 et seq in Thomas, P.D. (1952).
Conformal Projections in Geodesy and Cartography. Special Publication No 251. US Department of Commerce.
A further disadvantage of using skew coordinates (i.e. geocentric latitude) is that each point on the height axis has a different latitude, except at the equator and poles.