Like e.g. the education system, especially the amount of years spent on education before starting to work

Exactly. It’s kinda hard to spend years on education, years building a nest egg, when you haven’t spent all that many years alive.

The correlation is through socioeconomic conditions, correct. Older parents have worked longer, saved more, and can provide greater opportunities to their children, which in turn creates a more prosperous society that values education, social security, etc.