This is a great way of putting it, and I think about this a lot.
My wife's ancestors had kids at younger ages, and my ancestors had kids at later ages. Her grandparents are all still alive, mine have all been gone for more than ten years.
My spouse and I are on track to have kids in our mid/late 30s. My wife's parents are both in their mid 50s, and realistically they'll probably have 20 years of overlap with our children.
My parents, though, are in their mid 70s. I have to hope they have at least another 10 years of good health so that they can forge a bond with our children. Even with good health, though, the way a 75-year old interacts with a young kid is going to be very different from the way a 55-year old does.
I made the same choice as my parents and will likely face the same future, where I may have little or no overlap with my grandchildren. Since my generation has delayed childbearing for so long, I think this is something we'll see largely as a mistake in about 20-30 years.