My impression is that it came more from the early Scots-Irish settlers, who brought with them the very similar tradition that exists, for example, in the Scottish Highlands (where you had a lot of remote houses that made hospitality to travelers essential).

I've spent a lot of time in the Scotland of my ancestors. And it's the only place I've ever seen the same tradition of "hospitality" (both use the same word). When I first experienced it, I thought: Oh, now I know where the South gets it. The Highlanders didn't have slaves, so my sense is that while the servants and slaves reinforced the tradition in the South, it didn't start with them.

There's probably a scholar who has researched and definitely identified the origins of the hospitality tradition, though. So what I've said is just what I've observed in both the Scotland and the South.