Concert films are constantly at war with themselves. If the musical act is transcendent, then a filmed document will never come close to reproducing the experience of seeing and hearing the act live, in the same way that an ordinary photograph can only serve, at best, as a reminder of a moment. Even a great, exact reproduction is still just a copy, not the original. If the act is merely average or worse, then why bother to record it?
The Rolling Stones have been captured performing in concert on film or tape numerous times, so the challenge that lay before Martin Scorsese was to do something different. After all, this is the man who redefined concert films with The Last Waltz in 1978, in which he eschewed the prevailing wisdom that a concert had to include generous allotments of time devoted to the concert goer's point of view. Instead, Scorsese kept the action tightly focused on the stage, allowing the audience to enjoy the interplay between the members of The Band and various guests who shared in the group's final performance. He balanced that with lively interviews; in the process, he helped to establish Robbie Robertson as a viable solo personality in the eyes of the film industry.
I should amend the previous paragraph to read like this: "The challenge that lay before Martin Scorsese was to do something different or so I thought!" As it turns out, my expectations for Shine a Light were far too high.