I don't understand this misconception that handedness should always dictate which wing a player is on. In the defensive zone, when the opposition has the puck, it's more advantageous to play on the off-wing. Of course, as soon as the puck changes possession and the skaters head the other direction, the opposite becomes true. Then in the offensive zone, the off-wing is better for shooting, while the strong side is best for protecting the puck. The benefits become situational down to the second.
But I'll never buy that playing on the off-wing handicaps a player defensively in the least. Three-time Selke winner Jere Lehtinen preferred his off-wing, too.