Please keep in mind, if you had a cartridge box for your milita duty you kept it at home with "60 rounds of ball & powder. And a well scoured bayonet or tomahawk" (from Crown regulations for Militia 1750). Now part of your "training" was to use this powder and ball to hunt. You tended to claim the powder "lost due to water" and draw new issue periodically.
Also regulars and militia who have served their commitment and been released by the Crown, they kept their issued arms as part of their payout. If they were paid in land for their service as well, it tended to be on the frontier. Giving you trained experienced cadre for your local militia there to keep order.
So long story short, at least up to the late 1780s cartidge boxes in "civilian hands" are not uncommon. The Crown "collecting" some of this equipment was what drove events such as the "battle road" in New England (Lexington and Concorde)