You rarely find seafood on a barbecue-joint menu for good reason. Unlike the muscular flavor and texture of pork and beef, the culinary qualities of seafood are more subtle.
Blasting a piece of fish with wave after wave of heat and smoke would yield predictable results. Imagine placing a filet of Dover sole next to a typical 12-pound brisket on the rack of an offset smoker and cooking it for 12 hours. The filet would mostly vaporize after 12 minutes, much less 12 hours.