Comment by webrender

Your last paragraph, I feel, is focusing too much on the individual, direct contribution and ignoring the effect a person staying at home can have on their family. By taking care of their auxilliary needs and letting them focus on their core tasks (work, school, etc.), the increase in productivity of the family as a whole can exceed that of a direct individual's contribution. I think of it as a project manager for the family - they don't directly contribute to the development of a project, but they handle the overhead that would otherwise thrash their developers.