I know a number of states allow children as young as 14 to get married with parental consent. On the other hand, how many states allow children under 18 to get married without parental consent (or, at minimum, a very severe vetting by a judge in an emancipation hearing)?
You are close to the core here. There is no question that children are sexual beings from a very early age. Most parents have probably had to confront the reality of their young children masturbating.
The question is not child sexuality. It is child responsibility. Children are sexual, but children are not responsible. The parent is responsible, and the results of child sexuality in unwanted pregnancys, potential disearse, exploitation, and emotional problems that children are just not ready to deal with, but the parent will have to, are a very real justification for parental contol over their children. Once a child is emancipated, then they are responsible for themselves, and they should be able to control their own bodies.