Also, I don't think there would be any need for this even in real life. The joystick depicted in the game is "right-handed" only in the sense that it's to be used with your right hand, not in the sense that it's only for right-handed people. It is perfectly possible for a right-handed person to easily learn to use a left-handed joystick, and likewise for a left-handed person to use a right-handed joystick. There's nothing inherently difficult about this.
(In fact, we have the perfect real-life example of this. It might not be exactly the same, but it's pretty damn close: Game controllers. They have a left half and a right half, and almost nobody has any difficulty using either half for its intended purpose, regardless of their handedness. Thumbsticks, buttons, triggers... all equally easily usable with either hand.)