Sex is essential to reproduction. It is no surprise that men and women are strongly motivated to have sex. Evolutionary psychology has a good story to tell about the finer points of human sexuality too.
Animals typically have a breeding season and mate in the moment based on instincts. Human sexuality is far more complicated. Many men are not that far from animals in basic outlook, being interested in sex just about any time, with just about any attractive female if society will not punish them.
Sex is ultimately just as vital to women, but they are far more discriminating. In most animal species, males provide nothing but sperm. Females are motivated to find males with the best genes, but it's a one-time decision. In contrast, human men in our environment of evolutionary adaptation provisioned their families. They still do today. When a marital bond is broken, the need is recognized and enforced by way of child support payments.
Pregnancy is more metabolically costly for women and risks death more than in other mammals. For a woman, mating with a man who stays around to provide for his children is success. Mating with a man who abandons her is failure -- sometimes catastrophic failure. It is no surprise that a desire to avoid abandonment is at the heart of female sexuality.
Most societies have solved this problem with the institution of marriage. Socially sanctioned commitment comes first, sex comes later.
But we live in more permissive times. Some women choose to have one-night stands and short-term relationships. But they choose it less often than men do. They also sometimes set out with that goal, but find that they care about their friends-with-benefits partner in a way they don't want to but can't help. Mostly they are looking for long-term relationships. A very common societal tale is the adult woman who has sex with a man on the assumption he wants a long-term relationship too. When she finds out in days or weeks that he never was, she feels deeply betrayed and hurt. In terms of costs today, there's no material harm to her in the common case where she used contraception or has access to abortion. But our psychology is shaped by the forces that were active in our evolution, not cost/benefit analysis today.
The importance of sex is also reflected in rape laws. Women must have sex to reproduce, of course. As noted before, sex with an inappropriate partner can have devastating consequences, so obviously they strongly want their judgments on the subject to be respected. They fear rape deeply and detest it.
Yet women have also faced selective pressure when they are partnered with a less desirable man to have sex secretly with a higher-status man. They have strong incentives to lie if such a liaison is discovered. If a woman was raped due to unfortunate circumstances, her established male partner can have a reasonable hope that it won't happen again. If she chose it, then he has far stronger grounds to doubt the paternity of past or future children and she risks abandonment. (This level of detail is speculation -- the role of genetics as opposed to culture is harder to judge.) This could support the counterintuitive findings that women who were overpowered and suffer physically during a rape are not clearly more traumatized than those who gave in to verbal coercion.
But even if you don't accept that explanation, for whatever complex of reasons, women have been known to lie or have faulty memories about just how willing or unwilling they were. Whether to convict a man of rape often depends on deciding who to believe on the subject of consent.
Let's return to adult-child sex.
To my mind, the single biggest benefit to age-of-consent laws is to resolve cases of indisputable rape. If it is agreed that sex took place, then a young teen girl does not need to prove lack of consent. Men know this and it deters rape. This restriction is workable because fewer underage girls do actually consent and because sex is not vital to their well-being.
But there are benefits to prohibiting sex between men and enthusiastic young teen girls as well. Adult-teen sex hardly ever leads to marriage today. For girls, the end of the relationship taps into their innate tendency to feel distress at abandonment. This explains how girls can be not traumatized but even enthusiastic about sex at the time and regret it later, but the change is not due to brainwashing by a prudish culture. The penalties for men who have sex with enthusiastic young teen girls should be less than if the girl says she was unwilling, but there are good reasons of social policy to deter a man from allowing such relationships to develop. (Of course some young teen girls agree to sex and never do come to regret it.)
How are things different for prepubescent children? The most dramatic difference is that they have no need for sex, and very few have any active desire for sex with another person.
Pro-contact pedophiles sometimes argue that since sexual stimulation feels good, people of any age ought to want it. In particular, if society wasn't so prudish, large numbers of prepubescents would be open to the advances of pedophiles. Since it's just a matter of what feels good, any long-term consequences are just vestiges of outdated restrictive morality. But it is plausible that the complicated adult female attitudes towards sex would already be in place during childhood instead of arising during puberty.
All that said, it is clear that the finer points of women's attitudes towards sex are shaped by culture rather than genetics. But there are grounds to suspect a genetic component -- that any effort to transform society so that sex is just something that feels good in the moment might ultimately be very difficult. The whole question is assuming that people came to feel such a change was desirable, which is of course a huge assumption.
Sex is special.