They are/were though. I'd say it's just more pronounced in the USA. British musicians have, I er the years, had an ability to take black music from across the Atlantic, tweak it, and send it back over to American audiences in a form they can more easily digest. The Stones whited up Blues music and influences scores of artists as a result.
I'm personally not a fan. They didn't have the explosive punk rock energy of The Who, and they weren't a band to write about big ideas in a provocative or interesting way. They didn't have the musical chops or the desire to expand their horizons like The Beatles. They didn't expand on the genre like Led Zeppelin. They just wrote a load of blues-rock songs that people like.
Even listening to contemporary bands like Black Sabbath, Pink Floyd, or Led Zeppelin, they'll all happily cite The Beatles as an influence, but it's the like of Aerosmith and Guns N Roses who are touting The Stones.
I think it's laughable when people sayi "The Beatles or The Stones. Half of the RS's songs blend together into one mid-tempo snoozefest for me, whilst I could hum you a hundred Beatles melodies.