Certainly desire is part of it. But to what end? The early stories about sex in the Bible are not about love or desire. They are about people being joined together. And they are about reproducing.
In the first place (Genesis 1) sex is implied as the means of multiplying the race. In the second place (Genesis 2) sex is the way the man and woman express their clinging to each other and form the bond that unites them as one flesh. It is hard to read that story in any other way than as a wonderful and pleasurable way for the man and woman to enjoy their union as flesh and blood humans.
Sexual relations and faithful love are two of the components of marriage. Faithful love is the cleaving, joining, clinging to each other referred to in Genesis 2. The other component is the leaving. Leaving parents, and forsaking all others who might be potential husbands or wives. Sex was given by God to be one of the set of bonds that make a marriage.
Much of the attention that sex gets in the Bible is meant to protect that marriage relationship. Prohibitions against adultery are the most obvious (see Proverbs 5). But all other sexual relationships are also prohibited for the good reason that sex is one of the crucial bonds of marriage and sexual relationships outside and apart from marriage will tend to weaken the marriage relationship.
There is another good reason and that is that sexual relations join a couple as one flesh. But outside of marriage they do so apart from the other strengthening bonds of marriage.
This results not only in sex being driven merely by desire, but that people’s bodies are also being used for satisfying desires. What’s wrong with that? some say. Apart from the fact that that is not how God made us to be, it also reduces us to objects of consumption instead of enriching us as partners in a union of the male and female that God intended us to be in marriage. It tends to give the power to desire as an end in itself instead of desire energising faithful love (see Song of Solomon).
Dale