I completely understand your point. They have released plenty of live albums but most of them have been well after their prime. There is a huge difference between hearing them as hungry, young and vital musicians as opposed to hearing them today. This one is very much when they were at or near their peak and all of the tracks are from 1968-1973. It does feature "Jumpin' Jack Flash" but there is no "(I Can't Get No) Satisfaction" to be found. Also, did I mention that Mick Taylor is featured? Mick Taylor!
Somewhat ironically a few of those live albums you mentioned arrived in the post today (Still Life, Stripped and No Security). I found them cheap and thought that it was time to plug the holes in my Rolling Stones collection.
"Stripped" is the best of those by far. The other two are routine Stones live albums. Not bad of course, but not outstanding either.