Thanks for a great question. Not only does it reclaim lost art, art therapy is often found to reclaim lost soul, or as Thomas Moore writes in Care of the Soul, "soullessness in the standardization of experience." The psychotherapy and academic psychology you refer to in your original question is often concerned with curing, getting rid of symptoms. Art therapy, along with depth psychology attempt to care rather than cure. Thomas Moore explains his stance in the abovementionned book: "I try to give what is problematic back to the person in a way that shows its necessity, even its value." It is a process that ideally restores appreciation for a client's complexity and idiosyncracies. Art making with an art therapist (and to a certain extent without one) helps to reveal this rich complexity.
More inspiring Moore quotes about what to avoid: "Shallow therapeutic manipulations aimed at restoring normality or tuning a life according to standards reduces--shrinks--that profound mystery to the pale dimensions of a social common denominator referred to as the adjusted personality."
Yep! As James Hillman, the founder of archetypal psychology, said so pointedly last time I heard him speak, "You can't fix it! And besides, it ain't broke."