I mention the other genres because a number of their songs really were not "rock" as they were originally written and arranged.   "Hound Dog" was a blues or r&b song written for Big Mama Thornton, and "Kansas City" was written specifically for West Coast blues/R&B artist Little Willie Littlefield (and also recorded as a blues by Peggy Lee). And a number of their songs, e.g., "Loving You," could hardly be called anything but pop.   I think that their versatility was a big part of their genius.