I’ve been teaching kickboxing now since 1998 and inititially started because the martial art school where I was training wanted to offer this type of a fitness class.
I was a 1st degree black belt at the time and had the knowledge to cue proper body alignment and technique, I had absolutely no experience with building choreographed combinations or routines structured to a 32 count block. Aside from that, I had little knowledge of anatomy and physiology.
I was certified to teach in a 2-day course to teach CardioKarate around the time that Tae Bo was popular but the course was offered through NAPMA for martial art instructors.
I wanted to expand my knowledge even further and eventually earned my group and personal trainer certification.
I have seen many martial art instructors teaching kickboxing with no group exercise certification and aerobic teachers teaching kickboxing with no martial art technique experience.
I really do think it depends on the nature and style of the program. In martial art schools, the classes are geared more to martial art technique (techniques to targets or freestanding bags) whereas in group exercise most classes focus on choreographed combos as in Tae Bo or Turbo Kick. Either kickboxing style can incur injuries if not properly instructed.