I don't think any one approach to bank fishing is that much more effective than another. Plunkers catch plenty of fish, and you can't get much more stationary than that. Others do fine going from hole to hole. It's more a factor of where the angler falls on the scale that goes from clinically dead to hyperactive; AND are the fish moving, or holed up. If they're moving, you might do well staying in one spot. If they are holed up, you probably should be moving.
HSL, you mentioned hunting, and the same question could be asked of that sport-- stand or move? In either sport, I like to move about. It's a metabolism thing. When I'm 95 years old, I'll build a plunking shack, and buy a tree stand