You've asked a very difficult question to answer. It seems that there's no specific reason--but banana pudding is considered the ultimate Southern dessert and a staple on soul food menus. The banana pudding phenomenon isn't exclusive to BBQ, it seems that pretty much any true Southern menu will feature some banana pudding.

This is a fairly recent Southern delicacy, as the earliest banana pudding recipes, and the appearance of Nabisco's Nilla Wafers weren't until about 1901-1902. Since then, it's taken off as a Southern favorite, but no one seems to know how!

I can speculate that because it is such a cool, light dessert that it goes well with the hot climate and heavy foods of the South. It's a nice compliment.

Also, seeing as some of the most prominent commercial banana producing countries are Mexico, Costa Rica, Brazil and Ecuador...from a geographic standpoint (especially in the early days of importing bananas), it makes sense that bananas were more readily available in the South.