"Exile" aside there are just so many contemporary bands that were better.
They aren't my favorite band from that era, but they still put out some great records. Exile isn't even my favorite of theirs.
Aftermath, Beggar's Banquet, Let It Bleed, and Sticky Fingers are all stone-cold classics and Goats Head Soup is extremely underrated. Their last worthwhile album was Some Girls in 1978.
From 66-73, they were pretty damn prolific.
Speaking of music from this era, I just discovered the 1970 album Cold Fact by Rodriguez last night and HOLY f*** my mind is blown. Psych-folk/Blues with Dylan-esque lyrics. I am questioning my entire life for not being aware of this album.