It may have been Pete's choice just to sing and not to speak. Pete is pretty careful about what he does and doesn't do these days, and with the documentary and the new CD, he's extremely busy. For someone like Pete, who's been doing this all of his life, it may take a lot more energy to banter with a talk show host than to just sing the song.
Obviously none of us know. I'm just grateful that he's still performing, at least a little, and that people like Letterman are giving him a national stage.
He is one of the wisest people I have ever encountered. That doesn't have anything to do with this thread; it's just true.