EVENSVILLE, Tenn.—The local Dollar General store, built on a rural highway and surrounded by farmland, sells no fresh meat, greens or fruit. Yet the 7,400-square-foot steel-sided store has most of what Eddie Watson needs.

The selection echoes a suburban drugstore chain, from shower curtains to breakfast cereal, toilet paper, plastic toys and camouflage-pattern socks. Refrigerators and freezers on one wall hold milk, eggs and frozen pizza.

Many...