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People continue to influence their children long after they stop reproducing. Genes that help you children have more children are selected for, so something like a gene that keeps you alive long enough to care for your grandchildren seems plausible.

Although there are also clear costs to this, and as you look at longer timescales the benefits become less pronounced.

I'd at least say I don't see a strong evolutionary pressure for extended lifespans.

Children might have better likelihood of eventual reproduction if their parents are in good health as the parents raise their children during and past the parent's reproductive age. I could even imagine present and healthy grandparents having an influence on the reproductive probabilistic success/failure of their grandchildren.

Long juvenile period. A 10yo human child with living parents has a greater chance of surviving to breeding age than the same aged child with dead ones.

Also, a reproductive pair with living post reproductive (but still not decrepit) parents can breed at a higher rate as they are can delegate some childcare to them.