From what I've seen - also careful to note that the plural of anecdote is not data - older parents are also more likely to "invest" in academic extracurriculars and such. In sports, there's a range of parental ages. In music lessons, it skews older. In robotics and computer programming activities, older still (with a noticeable geek-outlier subset). That could also contribute to the children of older parents developing more school-relevant skills at an early age.
Also, "red shirting" for academic reasons is something older and more affluent parents do. Younger and lower income parents look forward to the start of kindergarten as a break from high daycare bills or the everyday duties of having a child at home, while older parents seem to look more carefully at readiness. And it has been pretty well established that older kids perform better in the early grades and often get tracked onto higher-level academic paths before the simple developmental differences even out, giving them a more or less permanent advantage over their younger classmates.
I've been joking with my mom that this is why people her age don't have kids (she's 70 - they really don't!). She is forever worrying about things that my kids are doing, and I know for a fact that some of them didn't phase her one bit when my brother and I were younger. She's just gotten much, much more cautious with age, and my MIL is even worse. We're not even telling MIL about DD16 applying to a foreign exchange program because we know how she's going to react; she didn't like DD going to summer camp at Texas A&M and hates that she's looking at urban colleges because cities are so unsafe.