Its a great question. The concept of a case in a case was very common but way before the period we are talking about in post civil war America and especially with the advancement of technology late in the key wind era to stem wind and good environmental packaging to be implemented with effective dust covers and such. It is very common if you collect the early British Fuse pocket watches early 19th Century to find pair case or case in case packaging. I think it was done to enhance the effective usability of pocket watches in that era to rougher use and environments.
By the 1880s when this watch I own dates to a sturdy key or stem wind hinged half hunter with a solid dust cover and thick crystal really should be as good as it needed to get but there must have been some market demand because a few of these pair case or case in a case watches were still produced. My watch also has a thick bulls eye crystal which again is a sign the original buyer/owner was thinking of the old days pre 1850. But, really nice machining at the stem where the inner case fits into the outer case and to be honest when all put together it looks and feels like one watch not a case within a case as compared to the later period during WW1 where soldiers or industrial coal miners had an external case for their pocket watch to function in and not be affected by the hostile environment.
The watch on Oldtymers and the early Illinois I own are but a few that have this old style case in case packaging. The Oldtymers case is Ore Silver as is mine which suggests the rough expected use whomever the original buyer might have been back in that era anticipated....I have had it cleaned oiled and timed and its running nice....I initially bought this Illinois KW based on the case. I just have not seen many in my days collecting....