An interesting question when one considers swinging a sword is as anachronistic in the 21st century as using a square rigger as the primary mode of marine transportation. So, it begs the question "why would one study and practice a medieval fighting art, when people don't walk around with swords any more?"
The question can be answered two-fold: a) cultivating an appreciation and understanding of the medieval period and of a people in the time where individuals developed both defensive and offensive skills in sophisticated fighting arts not derived from Asian or Eastern cultures, but developed within the context of European cultures and b) developing defensive skills applicable in the 21st century. After all, there's more to swordplay than swinging a sword around. The fighting art encompasses a number of levels of physical skill, including grappling, dagger and other classic weapons of the medieval period. Training swordplay without the basis provided by close-quarters fighting is like learning how to drive by using a Formula 1000 race car. There's a ton of material to become familiar with and skills to develop before taking that F1000 to the track!
Personal evolution through enhancement of one's intellect through expanding it to encompass a historical period is invaluable to anyone seeking to grow. When one takes the historical component and applies it to a real application such as medieval martial arts, what better marriage than the intellect with the physical?