With my current AAU class almost over and Online Workshops always busy I do get to see a lot of shots and reels, and I answer a lot of the same questions. One of the topics involves dancing and martial arts shots.
Now, this is purely subjective, but here are my 2 cents:
I personally would not do a martial arts nor a dance shot, as those types of shots are not really useful on a reel, if the company you're applying to focuses more on performanes. A dance is just motion. At least dancing really forces you to pay attention to timing. But it's just not interesting to watch. Same with martial arts. It's okay if you just want to learn spacing, arcs, posing and timing. I know, that's a big chunk that you obviously shouldn't skip in your learning process, but when things are just moving around without any thought behind it, I'm bored.
The most interesting thing in a shot facing a character is conflict, or in other words, a problem. When someone is faced with a problem, they have to make a choice and that choice tells us something about her/his/its character.
And that's what this is about, character animation. We want to see thought process, thinking, decision making in a character. For me that's when characters are truly alive.
Again, as exercises those two type of shots are fine. Practice makes perfect and both will help you master body mechanics. But when a character is just moving around without any personality and thought process behind it, then I wouldn't have it on a reel.
You could introduce a problem to the character while she/he/it is dancing/martial artsing. :)
Conflict adds a lot of interest, to any kind of situation: