A thought which has been loitering for a while:
If we become fertile mid-teens, for most of our species' history this is the time that we'll have started having children.
That means that by the time we are mid-thirties, for most of our species' history, our children will have begun raising their own kids, and we will be starting to fulfil the role of grandparents.
The most well-adjusted child would presumably be the one whose parents, and also whose grandparents, were committed to its welfare. A stable lineage would therefore be more likely to evolve than an unstable one.
The physiology and, as a consequence, psychology behind good grandparenting would over time evolve.
Just as we prepare to become parents as teenagers, we prepare to become grandparents in our thirties. This is also the time that boys in Africa become fully grown men, and people in the West undergo career changes and feel the pressures associated with a midlife crisis.
What if the mid-life crisis is about equipping us to become Grandparents, to the tribe, if not to individual children? A forced change in perspective, away from the direct learning of childhood and early adulthood, towards a frame of mind where what has been learnt is now to be shared with younger generations. If this role was fostered in society, a kind of informal eldership, from mid-thirties onwards, would the impact of middle-age be smoothed away?
If it's natural, my guess is it is happening anyway, and the evidence is probably there in pop culture and stories.