The initial bad side to having a large npc family might be inheritance laws. I would say that one stands out clearly as the biggest potential issue with having a large family.
If we can use the npc's of our family as workers, then I would use as many of them as possible as cheap labor.
There will be more details to come though that could lead to more negatives and positives being realized. Perhaps having more of your bloodline get accepted into some Noble's armed forces would mean that your family bloodline as a whole gains more reputation in that domain.
Perhaps with more children you can send one as an emissary to someone else that you wish to have business with but perhaps that child doesn't have the proper stats to have a good conversation with said person so the meeting actually goes bad and thus you don't gain any business from them. With less children, you might have went and did that yourself and found success.
It's too early to tell but I myself am leaning towards creating a large locked bloodline. Eventually there will be other players that I might trust to join the family and further spread it's name. That is the hopeful side of me.