If I were to make a list of the top groups/performers during the critical 1964-1973 period, no doubt the Stones would make the top five handily, perhaps the top three. They also belong to that select tier with more than six excellent and important albums. They probably have created more great and memorable riffs than any other rock and roll group, ever.
So I don’t think I am unappreciative. My favorite cuts are probably the acoustic country songs on “Beggars Banquet’ and “Let It Bleed,” plus the riff-based songs from the mid- to late-1960s, such as “Under My Thumb” or “19th Nervous Breakdown.”
Still, I have not heard anything new in a Rolling Stones song for more than twenty years. I don’t mean that their later work is worse (though it is, much, for forty plus years running), rather I don’t hear anything new in their very best work and thus repeated re-listening is a waste of time. I don’t enjoy it.
In contrast, I’ve been listening to Jimi Hendrix for about forty years and still hear new bits in his songs most of the time. I am almost always excited to hear this work again.
I have two other objections. First, most (all?) of their blues covers are worse than the originals (the Beatles’ “Money” and “You Really Got a Hold On Me” and “Long Tall Sally” are all improvements, in contrast, not to mention John Lennon’s “Be Bop a Lula” or Hendrix’s “Hey Joe”). Second, you don’t have to invoke political correctness to feel that a lot of the early misogyny has worn thin and aged poorly.
So the Stones are boring, mostly, though still excellent in the abstract. It’s hard to imagine classic rock and roll, or the 1960s, without them. But in terms of lasting overall aesthetic merit they are just a wee bit closer to The Who than you might like to think.