Modern martial-arts instruction is super-regional. Not to go too far into the weeds . . . but as part of my day job, I worked on several peer-reviewed books on the martial arts with a man who'd studied boxing, kachin bando, kali silat, karate (goju-ryu and shorin-ryu), submission grappling, and wing chun, and who moved to Japan to fight in the SHOOTO organization (a kind of MMA) and earn his kendo black belt. Anyway, one of his favorite pastimes in discussions of the martial arts was talking about how "interpretations" vary radically from teacher to teacher and town to town, never mind country to country.
To get somewhat on topic: He loved music. He also informed me that in decades of studies in many countries, he had met unusually few martial artists who were above-average at music – or at dance. Grounding helps dance a lot, but he seemed to feel that most martial arts instill reflexes that fight against musicality. His theory was that drilling in being unpredictable in a match, in not falling into "beats" or "patterns" when a prize is on the line, drums that out of a person. Take that as you will. The exception is apparently capoeira, which is essentially a dance first.
Of course, this guy also laughed off aikido, claiming that you should study aikijutsu or go home. Take that as you will, too. It's possible that his predilection for full-force beating people up in the name of prizes (or getting beaten up . . . he had many injuries) colored his view. Maybe more peaceful, "internal" arts and do forms are useful to dance in ways that "external" arts and jutsu forms are not.
Hey, Bruce Lee had the same idea about ballet! 
