Chelsea i think you nailed it
and more, not even they were so unkind to media and press (i.e. common people opinion) not to be, literally, dead and gone, but were so rude they did not put up some glasses on, change haircut, act like "mature rock intellectual prophets with an art message" (i'm thinking of lou reed right now), instead they keep on rock and rolling and, how baffling for the press and the public opinion leads, they were consistent and solid about it when it comes to live performing. Sure there have been backdrops to this longevity in terms of writing and studio recordings creativity.
But this magic effect on anyone who happen to be close to their stage cannot be denied. I witnessed my wife who, though we've been to many concerts since we met 13 years ago, 1) does not like rock particularly, 2) does not like crowded and noisy live acts but like better club or theatre "listening to the music" performing, 3) is not particularly impressed (to say the least
by macho lyrics of our sir Mick...well, she was dancing and bouncing with me in Paris, Bercy 2003 (not 1972!) telling me and everyone after, how that show was so fun and how the band impressed her for "being in their music and happy to be on stage", their pleasure in playing, she says, is addictive and like a virus that takes you over and you can't--don't want to be cured of.
And you know, i don't think you can't air this on FM!