It may have gone out of fashion, but that is one of the ways we were trained to sling our shotguns in the academy and we used it fairly often. The idea was that it kept your barrel pointed in a safe direction while allowing unimpeded access to your sidearm should things unexpectedly ramp up again. It also allowed you to perform tasks with your strong hand without without getting in the way, while allowing you to transition to back to the shotgun if desired.
I do not know the history of the technique, but it may have been intended primarily for shooters who also had a holstered sidearm on their hip. I doubt it's still taught in many academies, because a large number of departments no longer issue shotguns, but it was an accepted technique in the past. All the departments in my area transitioned to AR's about a decade ago, so slinging a shotgun is a lost art, with the exception of certain specific SWAT applications (breaching, less-than-lethal, etc.). I'm too far removed to know exactly what they do these days.
