I wonder if certain Muppeteers had something special in them for performing musicians. Jerry Nelson and Jim Henson played a lot of musicians (Robin/Floyd/Gobo, Rowlf/Dr. Teeth/Kermit/Ernie respectively) and Frank's characters sang about as well as me (and that's not a good thing, trust me.) Richard had some decent characters as well. Dave not so much and Steve even less so.
"Sax and Violence" earned a special place in my heart precisely for the two reasons already listed- Zoot's impeccable timing and resistance to Mahna Mahna. Also, Zoot and Mahna Mahna might well be the two Muppets now most specifically associated to one sketch ("Sax and Violence" and "Mahna Mahna").
"Forgive me Charlie Parker, wherever you are!"