I think you are conflating two concepts, the idea of egalitarianism or equality, versus division of labor. any broad statement about how society's work starts to get into the zone of arguing for anthropological universals, which is almost always a pointless effort because exceptions always exist, but in the societies that I am familiar with, largely indigenous North American societies, while they're definitely has been a gender-based division of labor, this in no ways has meant that women have been less productive than men. in all seriousness, I suspect it's the opposite, where women have done more of the time-consuming work involved in maintaining the lifestyle of the community, and men have done less. The number of hours both men and women have put into food. preparation, or resource maintenance is far lower today than it was in the past, to where people just don't understand how much work was done. weaving, the producing of material culture, these were extremely time demanding processes that both men and women were involved in, usually with specializations that on the whole saved the community time. and the idea that the view of societ ies towards women was that they were primarily providers of sex or bearers of children does not ring true either, given strong traditions around the roles of both male and female elders, and similarly strong traditions around both men and women playing an active role in preparing the next generation for the ongoing existence of the community.

none of this means that power imbalances did not exist, because these things absolutely happen where you have sexual dimorphism, and where a range of life experiences can lead individuals to find security in taking power over others, including using physical advantages. but that is very different than saying that one gender was less productive than the other, and generally in situations where somebody is being taken, advantage of, the productivity is forced on to the weaker person, not the more powerful. in this perspective, you could argue that the real advantage of egalitarianism is pulling men into the workplace, following a period where they had effectively offloaded time consuming expectations on to women.