I do not believe that.
You raise an interesting question. Why might my grandfather’s statement be true or false? He would have been referring to the nineteenth century. Most Americans and in other countries average people lived on farms...subsistence farming. Children were viewed as free labor. (We have fewer children today because children are no longer a source of money, but instead cost money.)
“On average, woman during the 19th century had seven children - and some had more than twelve. Although the exact figures will vary depending on geographic location and local culture, it’s safe to say that families of the 19th century were much larger than those of today.” (historynewsnetwork.org/article/35975)
Other articles set the number between seven and twelve.
“Fatal Years is the first systematic study of child mortality in the United States in the late nineteenth century. Exploiting newly discovered data from the 1900 Census of Population, Samuel Preston and Michael Haines present their findings in a volume that is not only a pioneering work of demography but also an accessible and moving historical narrative. Despite having a rich, well-fed, and highly literate population, the United States had exceptionally high child-mortality levels during this period: nearly one out of every five children died before the age of five.” (Fatal Years - Child Mortality in Late Nineteenth Century America Hardcover )
If I recall the rest of the conversation, as a parent you didn’t want to be emotionally invested in a child if you’d already buried a couple of them, like during an outbreak of Yellow Fever, for example. Also, I suspect they viewed them differently. Probably around 1890 my father’s mother was literally sold by her father after her mother died. This was to a farmer in Sweden. My father and his family emigrated to the US in 1925. My grandmother lived in the farmer’s barn and took care of the animals. Definitely, things were different in the nineteenth century.
I know of a case where the only reason a boy was officially named when he was 6 was that the school board insisted on it. This wasn’t in Hooten Hollow either but Washington DC in 1930.