I would imagine they added some structural strength to the side panel, especially on the more slender guns.
not much if any. not really needed in that area of the stock considering the tang bolt and the amount of wood there as compared to the barrel channel where it can get wafer thin. with the aesthetics of really slim stock wrists behind the tang bolt and before the stock comb in vogue on lots of those 18th century long guns, that's an area of the wood that seems to get lots of break repairs.
I was thinking more in terms of supporting the lock. With thinner sides typical of earlier guns, the screws would be more susceptible to pulling through. Later guns like Hawkens had thicker sidewalls in the lock area and could get away with simple washers.
