A major misconception about Into the Woods is that the authors were inspired by Bruno Bettelheim's book The Uses of Enchantment. It's worth looking into the sources of this misconception and what Sondheim and Lapine have actually said about how and whether influence Bettelheim's book influenced the creation of the show.
Before Into the Woods started previews on Broadway, there was an article on it in the Sunday New York Times that included this passage
"As he worked on fleshing out the individual characters, Mr. Lapine not only drew on his own knowledge of Freud and Jung (one of his early plays, 'Twelve Dreams,' explored, among other things, the split between the two schools of analytic theory), he also read studies by such authors as the child psychologist Bruno Bettelheim, the Jungian theorist Marie-Louise von Franz and folklorists Iona and Peter Opie."
Frank Rich's review of the original Broadway production also mentioned Bettelheim:
"One needn't necessarily have read Bruno Bettelheim's classic Freudian analysis to realize that, in remaking Grimm stories, Mr. Sondheim's lyrics and Mr. Lapine's book tap into the psychological mother lode from which so much of life and literature spring."
When the commercial video of the original Broadway production was first broadcast, there was a segment at the end in which Sondheim and Lapine were interviewed by Edwin Newman. Lapine himself mentioned Bettelheim briefly in this interview.
"One of the reasons I liked writing it was because as I read the fairy tales as an adult, I could see how you could take the opposite point of view, you could read Bettelheim and find out the great message that they have but you could also read 'Jack and the Beanstalk' and look at Jack as something of a thief, and Cinderella as an imposter."
Betteleheim was also mentioned in passing in Stephen Banfield's article in the souvenir program for the original London production. In Craig Zadan's Sondheim &. Co., we find this: "Lapine consulted a psychologist and read studies like Bruno Bettelheim's The Uses of Enchantment."
But then we find this. On page 2 of an interview with Edward Seckerson, we find this from Sondheim:
"[W]e took a Jungian approach. You know, this whole thing about how we based it on Bruno Bettelheim is nonsense — it’s nothing to do with Bettelheim. In fact, I don’t know if James read the book, I didn’t."
And when Sondheim was interviewed by James Lipton for the TV series Inside the Actors Studio, Lipton brought up Bettelheim: "There seems to be a philosophical war in that musical between the theories of Bruno Bettelheim and Jung."
Sondheim responded, "It’s interesting you say that. Everybody assumes we were influenced by Bruno Bettelheim. But if there’s any outside influence, it’s Jung. James is interested in Jung—Twelve Dreams is based on a case Jung wrote about. In fact, we spoke to a Jungian analyst about fairy tales."
In a 1988 issue of the Performing Arts Journal, Lapine said this: "The Narrator is what the fairy tale is about. I tried telling the stories withouta narrator and it just doesn't work. A story needs a storyteller, and the storyteller is the ultimate figure of authority. Originally we wanted a public figure, not an actor, to play the Narrator: Walter Cronkite, or Tip O'Neill—someone who disseminated information and points of view. Then when we got rid of him you would see that the news was now being reported by the newsmakers, not the news reporter; decisions were being made by the people, not the politicians. Ultimately, we defined our narrator as a kind of intellectual, a Bettelheim figure; I wanted to get rid of Bettelheim!"
So it seems that even though Lapine had read The Uses of Enchantment, he regarded it somewhat negatively.