I see your point. Two things:
- the first Stones LP was mostly covers of American blues compositions. It wasn’t until the 2nd to 3rd LP that originals by Jagger/Richards, at the urging of Oldham, I believe, started to predominate. Because they released their first 6 LPs within 2 years, there’s really not that much of a meaningful start lag behind Lennon/McCartney.
- Beggars Banquet, Let it Bleed, Sticky Fingers, and Exile on Main Street are thought of as the Stones canonic high point, but I throw Aftermath - the first LP with all original compositions - in there as well.