Which musicians fits this description? one of the first masters of the walking bass, his association with basie goes back to the 1920s. he possessed a superb sense of timing that promote the bass to its role as principal timekeeper in the band.

it seems to me that yes they solo on the chord changes.  coltrane for sure solos on the chord changes. instead of changing scales, they use a different method over the chord changes. this melody is very  unique but may often times even be considered simple, which is quite common in this modal  type. for example, there are changes from the key of minor to major in this piece, which makes it  unique in its own way.