As part of the deep relationship between organic and cultural evolution, the history of the cultural versions of these fields seems likely to mirror what happened in the organic domain - though it is widely observed that cultural evolution and memetics suffer from a large scientific lag.
In the organic realm, group selection was popular until the 1960s - when it was practically wiped out by kin selection. At the moment, cultural group selection is a popular form of explanation. My expectation is that it will be largely wiped out by cultural kin selection.
If modern forms of kin selection and group selection make the same predictions, why is kin selection better?
The advantage of using kin selection is partly down to a difference in emphasis. The term "kin selection" emphasizes close relatedness - which is an important factor in why the theory works. The term "group selection" makes no mention of family or relatedness. This seems to cause group selection enthusiasts to neglect the significance of relatedness - and then go off the rails.
Group selection is probably more popular initially because it is easier to understand and apply. Without quantifying relatedness, armchair theorists are free to speculate about traits being adaptive at various different levels. However, for group selection, this ease of application also contains the seeds of its downfall. Scientists love to measure things, and kin selection's famous
c encourages quantification. This leads to more rigorous science. It also gives kin selection a higher status among scientists.
In the organic realm, kin selection won out in the 1960s and 1970s. However in the social sciences, many researchers in the domain of cultural evolution - Richerson, Boyd, Bowles, Gintis, Sober and Henrich and Turchin - have adopted the term "group selection" - despite the fact that the term is historically mired in confusion and misunderstandings and has led to a substantial body of junk science. Practically the whole of the rest of the evolutionary biology establishment prefers the kin selection framework instead. Kin selection pushed group selection into the scientific fringes.
I think the most obvious hypothesis to explain the situation is that the social scientists are lagging behind the times. Cultural evolution's scientific lag explains the observed phenomena neatly. The social scientists are about forty years behind the times. The idea of cultural evolution having a scientific lag predicts that the current enthusiasm for cultural group selection will be largely replaced by a substantial blossoming of cultural kin selection.
The coming displacement also makes sense after looking at the way in which the theories have been applied to date. The group selection theorists have only scratched the surface of the topic - concentrating on large-scale conflict between human groups. However cultural kin selection has a vastly broader domain of applicability than this. The group selection theorists fail to concentrate on close relationships. Yet this is precisely where theory predicts that the largest effects will be found. The enormous significance of close cultural kin has been largely ignored. There's a wealth of material relating to cultural resource allocation and cultural parental care, which kin selection illuminates better than group selection does. The approach based on group selection approach has been tried by social scientists - and the results are in. The approach has been a miserable failure. Cultural kin selection will be vastly superior by a wide range of metrics.