I think it varies by region, in Texas, I think you still see places that do simple menus, because they sell well, and there is little demand for more. I also think that the culture remains largely driven by a single tradition.
In the San Francisco Bay Area, it is a rare BBQ place that can really make money, and forget it in the major metro areas, you need to pull a large quantity of people, broad based appeal, and that means a larger menu is needed. Simply, many of the decision makers are the picky eaters, and they drive business to menus that are not meat centric.
Back when I was a kid, the man who taught me a lot about what BBQ is, ran two shops, one that sold just fried catfish, hushpuppies and slaw. The other, sold brisket, sausage, ribs and pulled pork, beans, cornbread and corn. You wanted slaw, you had to walk out of the BBQ place, around the front of the building and into the fish shop.