However, it does make a little more difference with a sword, since the dominant hand and arm is stronger generally and so a blow will carry more strength when delivered that way. But R2's right, they probably just make everyone right-handed to simplify animation.
I'm more of a lurker, but this really interested me. This is coming from a fencer who can fence both dominant and non-dominant sides (I'm also a switch-hitter in baseball, but that doesn't have swords in it—usually). Now, maybe it's different when using actual swords or SCA type stuff than it is fencing, but from the sport fencing side of things, the problem isn't strength, it's more accuracy and finesse and being able to use tactics properly when it comes to switching hands and not being ambidextrous. If you can't properly use tactics, if you lose your finesse and accuracy and ability to perform footwork, you aren't going to land that hit, so it won't matter how strong it is.
The dominant arm is generally stronger because it's used more since it's the dominant arm. The non-dominant arm can be trained and strengthened to match the dominant arm in strength. With swords/fencing, the problem with using the non-dominant hand when you aren't truly ambidextrous is a matter of timing, reaction, instinct vs. you have to think just a tiny bit, and that non-dominant hand is always going to feel a tiny bit awkward while fighting/fencing no matter how much you train. You also have to add in footwork—your lead foot is going to change, your pivot is going to change, the distance you're most used to maintaining is even going to change. And you'll have to think about it since it's far less instinctive when you're using your non-dominant hand. Thinking is, well, bad. You want reactions and planning and strategies to be instinctive. You don't think, exactly. Well, you sort of do. You just do it so quickly from training and practice that you aren't aware of it, if that makes sense. But you switch hands and suddenly you're aware of thinking. You can mostly train it away. Mostly. But unless you're truly ambidextrous and both sides feel equally as comfortable, the non-dominant hand will always have that tiny bit of awkward.
I wonder how much complaining Cullen (or any of the melee fighters) would do if they were injured enough to have to switch hands and re-learn a lot of things. Though I imagine, say, Cassandra would have more of a vocal reaction to it than Cullen.