Just because your card is limited to certain merchants, doesn't mean merchants outside of that don't have products that's beneficial to your health. For example, gym memberships and multi-vitamins/supplements aren't typically HSA eligible expenses, does that men they aren't beneficial to your health? The same goes with CS, there are a lot of expenses that may not be considered related to a child's well-being but are certainly important.
What if the child needs a tutor, swimming lessons, music lessons, etc? ON TOP of everyday expenses these things are difficult to pay for, is it "wrong" for the mother to use the CS money for these things?Is it wrong for the mother to use CS to pay for the car repairs so she can get her child from A to B?