No, because you can read many inconsistent meanings into these stories. You need something else to justify settling on one. An example of someone who does this with remarkable success— finds a unifying meaning in a wide range of myths — is René Girard, in my opinion. But he both draws on ethnographic evidence and reads the stories in much closer detail than Peterson. Indeed his interpretation helps to illuminate elements in the stories that have been consistently overlooked, whereas Peterson’s interpretations require a lot of detail to be left aside.