The genre would be "martial arts reality shows". And it has been done. About four or five years ago there was a really lame show which pitted various types of martial artists together for "sparring" matches. I recall it embodying everything martial arts is NOT about, so I never really watched it.
Fight Quest and Human Weapon weren't exactly reality shows, more documentary, but I found them pretty entertaining, despite the inaccuracy of some of their "facts".
Both shows went to Israel to experience Krav Maga, which were great episodes.
In an episode of Human Weapon the hosts learned "Ninjutsu" and sparred with a couple of Hatsumi's 15th dans and essentially beat them both, if I recall correctly. I found it particularly entertaining.
The hosts from Fight Quest headed to Brazil to learn BJJ and one of the hosts was completely manhandled by Kyra Gracie.