I had the same question, but it looks like Apple simply don't allow it. I don't understand why - as long as the app asks parents to approve the addition of a card to an account, it should allow the child to add a DEBIT card. My son is 11 and has just opened a Nationwide current account, so in effect all offering Apple Pay does is give him a way of accessing his own money. It would actually make more sense to let him do this - while he's accessing his own funds, he's not using mine! Equally, he's getting used to managing his own money in the process.
Surely this is something Apple need to consider going forward?