Now it is true that the daycare model is in many ways more efficient than the traditional model but considering the ‘’happiness’’ cost and low birthrate associated with that model I think the traditional model will win every time, while still being pretty efficient.
In the day care model one person can look at 4 to 6 kids, while mom and dad both contribute to society; specialization at its highest and it is true that the traditional model cannot out do this model in pure efficiency. There are however some very high cost which will be paid for this level of efficiency. Children were not designed for daycare, children have been designed to get individual attention from their mothers throughout the day; especially toddlers.
Mothers were also not designed to be away from their offspring for long periods of time (but we cope better with this than children do). The result is that both children and parents are less happy than they could be when using this model and women fear becoming pregnant and doing it all over again; in part contributing to the lower birthrate we currently have.
In the traditional model women and men both still work but women prioritize their children and keep them close by while working. Society therefore receives the same level of productivity it has today (maybe even more), while keeping everyone happy. If women were to follow the traditional model and plan their careers around their children women would end up with jobs which are more flexible in nature. Jobs that require regular and strict attendance would be dominated by men and that is why I think society can potentially be more efficient using this model.
Women will have children regardless of what model society uses and when women take up a significant amount of places in jobs which are incompatible with motherhood women simply work less and take time away from those jobs for maternity and to spend more time with their children. Women also have less children in this model and more children leads to more successful societies. We also end up with less productivity in jobs that require regular attendance when mothers take time and years off. Most jobs are not like this though, but encouraging men and women to structure their lives in a way in which women prepare themselves for flexible jobs, while men gravitate towards jobs that have less flexibility in them can lead to a more efficient work force.
Another aspect of the traditional model that leads to efficiency is that males do better in a traditional setting and when males are doing academically better than females society as a whole is far more productive than when females are doing academically than males. This is the case since males never need to take time away from work for pregnancy or maternity related issues and males happiness level is less likely to be affected by a lack of constant bonding between them and their children. They also do not need to juggle pumping breast milk from their breast while working or worry about weaning and other child related matters which are exclusive to females (who have historically always dominated childcare and are the only ones capable of getting pregnant).
So in conclusion the traditional model is efficient because it allows specialization based on innate sexual differences. It allows women to specialize in jobs that are compatible with motherhood, while men specialize in the jobs which are not. This type of specialization can result in a society with higher birthrates and a workforce with a higher productivity level. It also allows for balance as in ensures that men and women both play a crucial and indispensable role in family life and that the needs of children are met in a biologically compatible way.