Here is where you are incorrect:
"Those persons, therefore, who have no legal capacity in point of intellect, to make a contract, cannot legally marry, as idiots, lunatics, and infants; males under the age of fourteen, and females under the age of twelve; and when minors over those ages marry, they must have the consent of their parents or guardians."
Adults can marry girls as young as 12 and boys as young as 14. It is legal in the US and elsewhere with the consent of parents or guardians. Also, pedophilia is not always committed without consent. Many actors and singers have taken brides under the age of 16 with the childs' parents' consent.