Who is the greatest rock and roll band of all time?

Good list, but you left off the Blues.
BB King or Muddy Waters. Honorable mention to Elmore James, Buddy Guy, and Albert Collins.

No music list is complete without including John Coltrane somewhere, so I'll put him at the head of the Jazz list, along with Buddy Rich.

Excellent choices. I didn't put Blues or Jazz because I was sticking to rock sub-genres. I did put "Blues Rock" (which again, drawing distinctions is difficult) and "Howlin' Wolf" is my pick while 70 era Chicago is my pick for jazz rock fusion.

I love Coltrane, but picking a greatest band or artist for jazz is something I would argue is utterly impossible.