1. It demonstrates that martial prowess has a unique potential to transform situations.
2. It transmits a set of values.
Whether your martial prowess is called "Weakness with a Twist" or "Bloody Elbow," it still demonstrates potency. Your martial arts performance can convey a wide range of different values, from extraordinary discipline, to winning is paramount, to never intensionally hurt someone--but it always communicates--it always transmits. In that sense, it always has a social function.
The film Redbelt is a must see!