Thanks for your comments,
I don't think that I outlined a purpose in marriage other than the equal recognition of the contribution of the man and the woman.
The need for that equal recognition comes from the unique needs of having children.
Its probably a small distinction, but to me it is very significant. Not the procreation itself, but the need of civilization (unique from a natural circumstance) on top of procreation.
And, I'm not saying it is a unique need for egalitarian recognition, many other relationship types have that demand -- and I believe an investigation will find they are all civilized types of relationships. My point in this is that it is most evident as a need, and as such perchance the seed of civilization itself, to recognize that in the complementary unification of man and woman and the establishment of responsibility passed between parents and child. It is part of what I meant that Eve may have been the mother of necessity for history, that decree of need is its own construct though rooted in specific natural processes.
There is no need for me, after outlying the separation of our species from direct dependance on nature (and that separation being civilization in a social-industrial sense), to require that kin altruism or egalitarian model should be recognized as natural to procreation (or as I understand your words "flows from procreation"). But the need is nonetheless naturally recognized and understood in urgency because of the natural products which combine to procreate and transfer the responsibility of civilization from one generation to the next. It is that union of civilization and natural that creates another intersection of duality that adds gravity to the notion of it being a seed of civilization itself.
I'll take an exception to one other matter where you say, "The bond is not a function of which genitalia we are equipped with." I'm not talking about dividing gender down to genitalia, nor do I find it a productive pursuit in understanding the full sum of meaning that a sexual bond has between two people.
Gender is much deeper then genitalia. Gender is itself a construct which is recognized psychologically, biologically, and genetically. A realization of this comes from asking yourself the question, could a gay guy have the same bond with a woman that he has with is partner? How about a lesbian with a man? Certainly the psyche plays an influence on the bond created, and it is heavily influenced by the gender (however identified psychologically) of the other person.
But this is just a mirror of the biological or genetic processing of those differences between a man and a woman which is the difference, categorically, between creating another human being or not, or other characteristics built into our species sexual dimorphism.
Another experiment, go to a Doctor and tell them you are infertile. If they ask you how you know this, say because you are in a gay relationship and haven't had a child yet. His response is likely that homosexuality and infertility are completely orthogonal. So an infertile couple requires a man and a woman, so does sterility.
Infertility can have an effect on that bond, so does gender, so do many other things which we understand and want in a romance.
I'm not saying what importance there should be on those differences, I'm just noting they exist.