It might not be what you think. From Stephanie Coontz’ book Marriage, a History: How Love Conquered Marriage (p. 31):
“Probably the single most important function of marriage through most of history, although it is almost completely eclipsed today, was its role in establishing cooperative relationships between families and communities.”
A few pages later, she adds that marriage has historically fulfilled a variety of functions in different societies, so much so that it’s hard to pin down exactly what marriage is. These functions also occur in different combinations, which could alternatively be performed by other institutions. The exception, according to Coontz, is not reproduction or even love, but the extended ties created through in-laws. Here is the whole quote:
In response to the Supreme Court’s ruling on the Defense of Marriage Act, Rosemary Joyce had an op-ed in today’s Los Angeles Times about an anthropologists perspective on marriage. In it, she emphasized two benefits of legalizing same-sex marriage for those who chose that route: status and dignity. Previously, she had written that definitions of marriage have never been static in any part of the world, and have been written and re-written over history. Today is no different.
Related: Humans Are (Blank)-ogamous, Part 1
.
Patrick F. Clarkin, Ph.D. 
Coontz is pretty much describing Lévi-Strauss’s atom of kinship—the exchange of a woman by her brother to another man.
but without the sexism
I don’t really look at it as an issue of sexist (when proclaimed by a male) or not sexist (when proclaimed by a female). I look at it as empirically demonstrated or not.
Friedl’s hypothetical custom of procreation (by “irregular encounters” of non-siblings, the children being raised by the mother and her siblings) is a pretty good description of the custom of the Mosuo people of South China.
They do seem to fit this description. Wonder if Friedl knew about them. A good short documentary on the Mosuo. http://www.youtube.com/watch?v=bbzG0n3shTM