When I took a jazz history course with Chuck Israels in 1974, he made a big thing of how Rollins and Thad Jones, as melodic-leaning improvisors, were much more attuned to Monk's music, as they really got inside the tunes, as opposed to someone like Charlie Rouse, who pretty much blew on the changes. Same can be said of Steve Lacy's approach to Monk.
I recently read Robin D G Kelley's biography of Monk where he reports that Monk was so keen that hornmen should continue to have the compostion in mind while soloing, that he was known to stop them in mid solo during public performance. This in mind, I was listening yesterday to Monk: Big Band and Quartet in Concert and thinking how Phil Woods certainly passed the Monk test, but that Rouse, who must have played more with Monk than any other hornman, did not. Strange!