Well, there is no doubt that the older bluesmen picked up on the white players - and Hendrix, of course, use of increased volume which in turn produced a richer tone ( and the white guys, and Hendrix, introduced effects pedals).
Of course, Buddy Guy says that he was the first player to really go in for very loud playing and distortion but, only live, because his record companies didn't think that Buddy's live sound would appeal to record buyers.
And, of course, the subject matter of white blues influenced bands appealed to a younger audience. They could identify with Satisfaction more readily than a Muddy Waters' song.