Yeah, I know there are tunes each of us would rather not hear or play again for a very long time. Our opinions, though, are not always shared by our audience (customers, financial supporters). It's fun in a jam session or song circle to moan about the over done material. In that setting we are among friends who understand our feelings. A public audience may not understand and I see no reason to insult them just so we can feel superior.
I think of the giants of traditional music forms whom I've seen in public and, to a person, none of them would allow their audience to feel slighted or insulted. They may not honor a request but they find a way of leting the requestor think they would love to do the tune if only there was time, or if only they had a Dobro player or whatever.
Bill Monroe used to ask for requests and, as members of the audience began shouting them out, he would simply wait until he heard one he felt like playing and honor that one. I can't think of any performer I admire who insulted the audience.
Listening to WSM on any given Saturday night, you might have heard Hank Snow singing "Movin' On," Roy Acuff singing "Great Speckled Bird," Mother Maybelle playing "Liberty," Bill Monroe singing "Blue Moon of Kentucky" and of course The Osborne Brothers singing "Rockey Top." Each of those songs must have long ceased to be musically interesting to such great performers but they knew what their audience wanted to hear and they were not going to let them be disappointed. I think that shows a lot of character.