Members of The Stones, Faces, Who, Led Zep, Eagles and many others had a tendency to let "off steam" while on tour.
I think it's great that the Stones are still touring at this level and drawing the audiences they do around the world. I know people who saw them playing at the Eel Pie Island club before they had a record deal and they have always been a fantastic live band.
Live there is no other band, but I wouldn't hold out much hope of a defining TV performance. They are in their 70's and the soundtrack probably won't be kind to them.