CIE L*a*b* was designed to measure color differences. The original Delta E metric (DE 1976), which is just the Euclidean distance, has many shortcomings which is why the CIE subsequently proposed DE 1994 and more recently DE 2000 to deal with the non-uniformities in the L*a*b* math. As Bruce Lindbloom explains on his site with examples, there are cases when moving along a straight line of constant hue angle in L*a*b* causes noticeable perceived hue shifts. This is not to say it can't be used successfully for image processing, but rather that it was not the original intent; furthermore, there have been more recent models that are better suited for image processing if "perceptual uniformity" or consistency is desired.
In some cases, image processing in a perceptually-uniform space makes sense, and other cases where it really doesn't. For example, some image processing operations assume (or work best on) linear light in which case using native camera RGB, GMCY, or some linear transformation thereof is the right thing to do.