One possibility would be for this activity to be undertaken by numerous private sector (and third sector) entities who would compete with each other to attract business and would adopt innovative (and hence diverse) approaches to child-rearing.
This raises the question of who the service is being provided for. If humans can be conceived and gestated in vitro (not currently feasible, but likely to be with advances in science), and then raised entirely in baby farms, there are no parents (or even adopted parents). So who is the service being provided for? The answer can only be society.
Perhaps the amazing revelation from looking at child rearing in this fashion is that parents throughout the world are effectively providing a free service to society by creating and nurturing the next generation.