What is the most viable type of family and why?
There is surely no one type of family that is more viable than all others in every situation. It is likely that the viability of a family depends more on the people in the family than it depends on the family structure. For example, while one might believe that a nuclear family is the most viable, there are clearly many pairs of parents who were not viable together.
I think that, in an ideal world, an extended family would be the most viable. An extended family would provide much more security and flexibility for all involved. It would be more viable if one member were to lose a job or get sick because the others could help that person economically. It would be more viable for children because there would surely be some members of the family that would always be available to play with them, to care for them, or to help them with things like homework.
However, this is not really viable in today’s modern culture. Therefore, I would argue that the nuclear family, for all its flaws, is the most viable family structure. It is typically superior to a single-parent family because it typically provides more economic and emotional support for the children and the parents. It is easier to get by if you have two salaries, or if you have one salary and a person who can provide day care and other services, than it is to get by on one salary alone. It is important for parents to have someone who is always there for them and supportive of them since parenting can be stressful. It gives children more role models and different sources of affection.
For these reasons, I think that a traditional nuclear family is more viable than others in more situations. However, this is not true for all cases and there will be plenty of blended families or single-parent families that do better than nuclear families.