Because it looks cooler in one hand and you can use your free hand to help maintain balance. You could also use two hands for power attacks. Elder Scrolls is a role playing game and some people would eventually like to play the role of a duelist, sacrificing strength and protection for agility and precision.
Exactly, it looks cool. You're right it's a roleplaying game, you're allowed to do anything you like, including things like imagining some random steel sword is your family ancestral sword and only use that for the rest of the game. Doesn't mean it should be as effective as using the best weapon available.
I'm sure it will be possible and somewhat viable to use a one handed weapon and nothing else, but I think it probably will be weaker than using something in the other hand, as it should be.
Duelists are good in duels, where your opponent has to follow the same rules you do.