Hi Tim,
That is a really good question and one I've wondered about myself!! I think by the time of the American long rifle, the 2-bolt side plate was more or less tradition. Obviously, it functions as a fancy washer for the bolts but the strength issue is very unclear to me. Sixteenth and 17th century matchlocks and wheelocks often, or perhaps even mostly, did not have them. They usually had nothing, washers, or some other type of decoration. So back that far, there did not seem to be any concern about strength without a big heavy side plate. I've considered 2 hypotheses. One is that tying the washers, whose use protecting the stock from the bolts is obvious, together in a single plate might reduce the risk of losing a washer when the bolts are removed for cleaning the gun. The second hypothesis is that the plate offered a large space for decoration. It is curious that muskets in the 18th century all had heavy side plates that got progressively smaller during the century, probably as a cost cutting measure. Eventually, they just had washers or in the case of British muskets, Lovell cups. I tend not to believe strength was ever the motive but rather tying the washers together and creating a canvas for decoration.
dave