In not-magic world (especially in movies), spies and cops often carry a backup gun in case they are disarmed during combat (the famous gun in the sock).
There are many examples in the books where a wizard or witch is disarmed during combat. All it takes is a simple expelliarmus spell. So it probably would be wise to carry a backup, wouldn't it?
Is there any canon example of a wizard or witch carrying a backup wand?