Massad Ayoob had a great perspective on the shotgun. He classifies it as the "artillery" gun, for when the family is all gathered in one spot and there is less need for the primary defender to move around. He refers to the handgun as the "infantry" gun - for use on the move.
I've always liked this school of thought. The shotgun is still a two-handed weapon, regardless. That other hand may be needed to open a door, use the phone, pull a loved one out of the way, fight off a bad guy etc.