The one free hand that you often see in depictions or re-enactments can represent a couple of things that aren't just for show and flair; parrying gloves were a thing that show up in a few places, and were essentially a mail glove designed to let you deflect and bat away the opponent's blade safely with your off-hand while leaving your blade line free to stay threatening. Alternatively, the practicality of keeping a free hand was sometimes done for versatility - it's much harder to grab a chair and brain someone with it with your free hand strapped up with a shield.

In the hands of nobility, it did certainly become a peacock fancy instead, but there are some practical roots buried back there.