Bureaucratic dehumanization is responsible for reinforcing traumas that cultures had already built ways of dealing with. My grandparents' generation reused the names of their children who didn't survive, but today, few couples would consider that with any name they were forced to write on both a birth and death certificate.
More common, perhaps, but I'm not so sure about the not notable part. There are plenty of examples of great grief surrounding the loss of a child. An example that comes to mind from my recent reading is Dostoevsky and "The Brothers Karamazov." The author was experiencing grief from the loss of a 3 year old son and the book rings with it.
However much the past is a different country, it is still populated by humans, same as any today.
There's some good poetic value in it, but I don't know if it's actually true. It has more to do with the effect it has for someone's "normal" life cycle, which is why orphan is only applied to children and not adults. And as the sibling comment mentions, it was pretty common in a family of ~5-10 to have at least one child die.