Neil Peart must be the John Bonham of his generation, as he is mentioned so many times in polls, particularly by non-musicians. No offense intended! Peart has his strengths, but he wasn't aware of his glaring weakness when he organized the recording of a tribute album to Buddy Rich after Buddy's death. Rich played mostly Big Band-style jazz, which is largely played in the "Swing" feel. Swing is pretty much like the "Shuffle" feel in blues.
Early Rock 'n' Roll, as played by Little Richard, for instance, often had a very pronounced Swing/Shuffle feel, but that pretty much died out in the 60's (in R & R; it lived on in Blues). Bands like Rush didn't incorporate any of the roots influences in their music, and apparently Neil Peart wasn't interested in learning how to play the Swing/Shuffle feel. That became obvious during the recording of the BR tribute album, when Peart's inability to play Buddy's music with the required Swing feel became quite obvious. It was very embarrassing to him amongst the drumming fraternity.