The US has solved the issue by requiring the consent of both parents (or proof that there is only one custodial parent/guardian) for the issuance of a passport to a minor. One-time form to fill out and the child's passport then serves as proof.

While letters can easily be forged and thus their protection is limited, it makes sense to always have a consent form as well as a power of attorney, valid in the destination country, for medical treatment and the like.