As feminist economists have long pointed out, households are factories in function and corporations in identity. They are factories because they apply human labour and tools to convert inputs like groceries, nappies, houses, etc. into things worth having, like meals, children, homes, etc. They are corporations because they are unified economic units, separated from the individualistic competitive market that operates outside its walls. That is, the individuals who make up a household, like the employees of any firm, are supposed to work together as colleagues to advance the success and prosperity of the corporate 'family' as a whole, rather than to advance their own individual material interests as actors in a market would.
Organising production inside the household - outside of 'the market' - makes economic sense in many circumstances, which is also why we have business firms. Using the market comes with significant transaction costs associated with establishing trust and quality assurance between self-regarding strangers. For lots of household work - like washing the dinner dishes - the costs of contracting with someone else to do it are so high that even though you have much more productive things to do with your time you are still better off doing it yourself.
More significantly, in addition to minimising transaction costs, corporate structures permit positive efficiency gains from coöperation. In particular, many projects - child-rearing for example, or soccer matches - are most economically achieved by team-work. A team works together on many-hands problems and thereby achieves much more than the same number of individuals operating by and for themselves could. One can't organise team-work through the market because it is impossible to identify and directly reward the marginal contribution of each worker to the final outcome (whether producing thriving children or winning a soccer match). The corollary of this is that team-work requires not only suspending the individualistic 'homo economicus' logic of the market, but also inculcating an ethic of self-abnegating commitment in which individuals adopt the common good or goals of their 'family' as their own, and do not shirk the sacrifices it requires of them. There are different psychological routes to establishing this disposition to self-less coöperation, including viewing the work itself as sacred or feeling bound by honour not to let down one's co-workers. But in the family it is generally achieved through love.
From a long and fascinating piece speculating on the impact of robots on family by the always interesting Thomas Rodham Wells.
It strikes me that we already have some directional test cases in the potential impact of robots on the family household because many wealthy people already outsource a lot of their childcare and home care to other people. This article observes the same but foresees a surprising forecast for the impact of decreased reliance on each other:
The arrival of cheap robot-servants will revolutionise the political economy of households. We will be able to produce consumption goods like meals and child-care much more efficiently since the number of human hours involved will be much less. That means the standard 'team' of two adults will no longer be required. There may not seem anything fundamentally new about this, since machines have been replacing human labour inside the home for a 100 years (e.g. washing machines). Such technologies have supported the social emancipation of women: less household work to do means more opportunity for higher status paid external employment. But they have also permitted the rapidly increasing number of single adult households. It turns out that when people can afford not to be mutually dependent on another person, not to have to love another, fewer of us do so.
Look, I've seen Wall-E, I know how this ends, with all of us as obese hedonists, fattened on a life of overflowing leisure, all physical drudgery having been offloaded onto an army of robots.
I suspect we're still a ways off from feeling a massive overabundance of leisure due to robot labor, though. Until my Roomba figures out how to cook me dinner, wash the dishes, and do my laundry, I have enough chores to fortify my moral fiber and keep me loyal to the household corporation.