@Jeruba That’s the one.
I was thinking of the usefulness of the object it terms of aiding the protagonist. If it’s essential use was simply that it was part of the plot you could say any character, place or object in a well constructed story served an essential purpose. While technically true, it isn’t essential in the way the asker meant.
The importance of obedience in fairy tales is the core of the prohibition/violation set up. The protagonist is warned that under no circumstance should they do something. With this set up the protagonist always ends up violating the one prohibition they have been given. Their failure to take advice or obey their elders, betters or whatever is the cause of the trouble they face. Therefore reinforcing that obedience is good and disobedience is dangerous.
The emphasis on obedience and use of prohibition/violation set ups are more common with female protagonists than male. It’s Red Riding Hood, Snow White, Blackbeard’s Bride and so on. Male characters’ acts of outright trickery and deceit on the other hand frequently bring them fame, fortune and the king’s daughter (Puss in Boots, the soldier in the Tinder-Box, the Valient Taylor and so on).
Personally I like the ones with clever girls, though even my favorite, Sweetheart Roland, kinda drops the ball at the end. It works out better if you chop off the end and transplant the end of Fundevogel (which is awesome). The stories have a common ancestor so they patch together rather effortlessly making a story better than either was on its own imho.
I have to agree the the economy of fairy tales is delightful. Aimee Bender replicates it in her collection Willful Creatures.