Puppets are magic. When used effectively, they connect with children in ways we can't anticipate or expect. My friend Suzanne's daughter had a long conversation with a turtle puppet like Billy--she told the puppet things she wouldn't tell her mother, though her mother was in fact manipulating the puppet. When my nephew was small, his puppet Fred had a conversation with my puppet Nigel on the phone. At one point he said, "Wait a minute, Fred, I want to say something." He took Fred off his hand and said what he needed to.
One of my favorite memories of puppet connection happened at a small festival at Haskell Indian Nations University about ten years ago. I was between performances (no, not Native American stories), walking around with Trixie on my hand. She said hello, shook hands, made small talk. She held hands with a little girl who was about four. The band on the stage began to play, so Trixie started to dance. She and the little girl held hands and swayed to the music, looking each other in the eye, not speaking, for about five minutes. Magic.