Not so until very recent human history. An interesting survey of the history of infant (under 1 year) and child (under 5 years) mortality reports:
According to the same article, as late as 1911, the United States had an infant mortality rate of 135 infant deaths per 1000 live births. Only three countries today, Angola, Afghanistan, and Mozambique, exceed that rate of infant deaths.
Kul C. Gautam of UNICEF puts contemporary child mortality rates [pdf] in perspective:
Gautam points out that the UN Millennium Development Goals, not only by directly working for children's health, but also by empowering women and improving sanitation, amount to a map for reducing deaths among children.
The parents of the Bemis infant twins above not only listed them on the large family monument, but also set up their own little stones, below.
Arthur and Charlotte were my mother's siblings, born and died before she was born.
My Aunt Steva's child never even received a name.
Even in the middle of the last century. ...And today...