Generally, when a family has financial issues, they will think of this thing themselves that they shouldn't have a lot of children because they won't be able to feed them all, but when a family has no such issues, they would barely think of the economic advantages or disadvantages unless there is an official rule of not having a lot of children.
I believe it has the positive and the negative like you have said also even from the family side. What happens in the family can affect or help the country but I think like the China example, it has helped their economy. Their large population help them to grow in technology faster than they would if only they were few because they increased in joining resources and creating research to grow their economy. Maybe now they have used family planning method to help reduce the rate of population growth but their numbers help to grow them also.
It has more manpower, and you are right, innovation in technology keeps improving because there are new smart people that are changing their current technology, but right now their policy, I think it is already ended, because they see that there are more old people in their country than young people, and also because people in China got used to the policy that others tend to not want to have a child. It seems positive to have fewer children than others, but in the long run, the country will suffer.