>Living for a long time after you have children is incredibly useful from the standpoint of genetic fitness. After all, grandparents play an important role in pretty much every human culture.
In the time scale that matters to evolution, grandparents played absolutely no role for the Homo Sapiens, and neither did culture.
I don't think that's at all likely. We've had fire and had the physiological adaptations enabling speech for well over a million years. We've been manufacturing complex tools such as spears with stone tips for about half a million years, to Homo heidelbergensis. Even Ergaster had lifespans allowing survival to an age where grandchildren could reach adulthood, allowing for skills transfer.
Do you have children? Raising children is hard. And it's a lot less hard when you have other adults to help. Historically, those would be grandparents and aunts/uncles. But aunts/uncles would probably have children of their own.
Nobody's saying that grandparents being alive are a prerequisite for grandchildren. But anybody with kids will tell you that grandparents are tremendously helpful in raising children.
Evolution is statistical in nature, not binary. Grandparents just have to be useful in raising grandchildren for them to be favored by natural selection. They don't need to be strictly necessary.
In the time scale that matters to evolution, grandparents played absolutely no role for the Homo Sapiens, and neither did culture.