Matt, a good question. The accordion was around in other rural American musical vernaculars -- see Cajun music, for example, among others -- but my theory has always been that the more rural climes and a lack of widespread adoption made maintenance and repair difficult, so even if one made it, chances of it being maintained properly are difficult, where as the string instruments that became popular are (relatively) non-specialized and easy(er) to fix.

Now, could you make the argument that the backwaters of Louisiana were any less hard on an accordion than the mountains? Certainly. That moves to my second thought, which is that more accordion-playing folks seem to have settled other areas, so there were more people to teach it, maintain and repair it, etc. This isn't necessarily exclusive to some areas -- Bill Monroe, the progenitor of bluegrass, had one in his original lineup (inspired by his mothers' playing), but quickly dropped the instrument after a few years.

I think most of all is that it just didn't appeal to their musical idiom in a way that lent itself to adoption in later eras. I understand that the autoharp, for example, was not nearly as widespread in the Appalachians before the folk revival, but did see a resurgence because it was a close enough musical analog that some people adopted it.