Indeed, we've incorporated sex into the artificialities of culture. That's why I spoke of sex in the widest sense, including dating, porn, fetishes, and so on. But the centerpiece is the biological act of intercourse, and that's precultural. The cultural appropriations of sex are the sites where the hypocrisy is most pronounced. Mind you, the hypocrisy is easily ignored since we're experts at suspending our disbelief and at playacting with mass trances.
But just think, for instance, of someone's buying of chocolates for his or her partner to celebrate Valentine's Day. That's a cultural act, but the insinuation is that the chocolates will please the partner and get him or her in the mood for intercourse. So culture takes us to the moon or enables us to build the Large Hadron Collider to learn about the Big Bang, and culture can ease our comfort level with having animal bodies with strained excuses. Seems pretty silly to me.
Obviously, culture can assimilate everything since culture consists mainly of fictions, and we can imagine fallacious and dubious excuses to extricate ourselves from any case of cognitive dissonance. Objectively, though, the more we attempt to make sex seem civilized, with cultural adoptions, the more we might be motivated by discomfort because of the hypocrisy I'm positing.