It has a factor when you are trying to get the puck out of the zone. I don't want to see Phillips/Boro/Gryba trying to do a weakass backhand when clearing the zone.
Also a big factor when puck is coming up the boards in the offensive zone. If D is on offhand, he has a much harder time to rim it back in on his backhand. Or else, he has to waste seconds transferring to forehand which by that time the other teams charging forward has already likely stolen the puck. Of course, the D could back off, but that means less possession and less offensive zone time.