I agree with your position on the Stones. No argument from me there.

But I don't think the Beatles quickly moved away from stealing from Black artists. They got sued by Chuck Berry's producer for their 1969 hit, "Come Together" for directly ripping off his lyrics. This was a year before they broke up in 1970. And although the following incident in 1968 involved a Nigerian musician, not an American musician, I find it particularly reprehensible:

https://en.wikipedia.org/wiki/Ob-La-Di,_Ob-La-Da#Background_and_inspiration

Brutal for McCartney to make a deal like that with someone in prison.