Not so many women as men die in warfare, it is true. But that is because they are often the object of the fighting. To be abducted as a sexual prize was almost certainly a common female fate in hunter-gatherer society. Forget the Garden of Eden; think Mad Max.
Constant warfare was necessary to keep population density down to one person per square mile. Farmers can live at 100 times that density. Hunter-gatherers may have been so lithe and healthy because the weak were dead. The invention of agriculture and the advent of settled society merely swapped high mortality for high morbidity, allowing people some relief from chronic warfare so they could at least grind out an existence, rather than being ground out of existence altogether.
Notice a close parallel with the industrial revolution. When rural peasants swapped their hovels for the textile mills of Lancashire, did it feel like an improvement? The Dickensian view is that factories replaced a rural idyll with urban misery, poverty, pollution and illness. Factories were indeed miserable and the urban poor were overworked and underfed. But they had flocked to take the jobs in factories often to get away from the cold, muddy, starving rural hell of their birth.