(1) More families lost children. This lessened the trauma because a family could talk to other nearby families who had experienced the same thing. Those families would also be able to give advice. In contrast, losing a child is extremely rare (in developed countries) today. This rarity breeds isolation, which makes everything worse.
(2) There were established societal and religious ways to deal specifically with the death of a child. Think prescribed ceremonies that grant a form of closure and which pretty much all of your friends and neighbors subscribe to. Nothing like this exists today.
To me, this is very similar to the suggested explanation in the featured article for why war used to cause less PTSD: there was less stigma around war, a much larger chunk of society fought in wars, and there were universal and well-defined rituals for processing the experience.
The whole thing raises interesting questions about our modern understanding of trauma. I think the most common modern statement on grief is that it's intensely personal and people should never feel that their grieving process is "wrong", at least not for a long time (years?) after the event. That at least seems different than past practice.