Child protagonist triumphs

When I first started attending a writing group, one of the rules I learned was: Always have the child protagonist solve the problem. Why? Because children like to read about children solving their own problems. In order for a child to solve a problem in a book, the parents and adults must be absent from the book. Let's look at some examples:

Harry Potter is sent to boarding school. The teachers offer some guidance, but don't solve the problems and often contribute to the conflict.

Katniss in The Hunger Games by Suzanne Collins loses her dad to a mining accident, hunts food for her mom and sister, and then is sent into an arena with 23 other children. Adults interfere and send awful plagues to torment her and the other tributes.

Anidora-Kilandra in The Goose Girl by Shannon Hale is sent to another country to wed the prince. On the way she is assaulted by her lady-in-waiting and abandoned by her protectors.
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Does the same rule apply in real life? Do children need to solve their own problems? Today was the first day of school for four of my five children. It's scary for me to send my children away to school. I can't be there to protect them, to answer their questions, to calm their fears. Last night, my nine-year-old daughter couldn't sleep because she was so unsettled about starting school. Should I just not send her? Then I was reminded today by my mother-in-law, who used to be a fourth-grade-teacher, that even teachers are scared of the first day of school. And both the teachers and the students live through it and triumph. Today when all four children return to me safely, we can review how they overcame the unknown and triumphed over the first day of school.