For most, there would be no benefit, and significant added expense. Since licensure is inherently a state-based activity, there is no reason to believe that licensing as an LPCC will make one's license more portable; in fact, a license obtained through grandparenting may have greater trouble getting recognized in another state. Add to that the still-unclear question of whether California will recognize national exams in counseling (national exams in MFT and Clinical Social Work are not recognized in the state), and the likelihood of a portability benefit grows even slimmer. The added expense of two renewal fees could be little more than wasted money.
There is, however, a legitimate reason why some MFTs may want to dually license: They want to reflect what their professional orientation has been all along. California was the first state in the US to license MFTs, and the last in the country to license LPCCs. As a result, some who work under the MFT license do so because that was the masters-level entry point into a career in mental health, and not because they particularly identify with systemic concepts. For those therapists, the Clinical Counselor license is probably a better fit.
They will not, however, want to switch over entirely. Counselors will enter the mental health marketplace in California more than four decades after MFTs did, and will need to fight for themselves every battle MFTs waged and won for recognition in hiring and reimbursement. They'll be able to make up ground, but it will be many years before counselors can claim the kind of recognition and stature in the state that MFTs claim today, thanks to decades of good work by CAMFT and AAMFT.