By this logic, culture and society would die every generation, and have to be rebuilt from scratch each time.
We all leave behind a "small" but far-reaching legacy that ripples out from our short lifetime. Each of the thousands of interactions we have with with other people and our general environment have a tiny but real impact that doesn't necessarily diminish to zero after we die. The change that occurs then has a small domino effect on any other person or system that it touches. And so on and so forth :)
My life today is deeply affected by the concerted actions of billions of unknown individuals from centuries and millennia past in ways that I can't even begin to fathom. I'm grateful for some of those impacts. For other impacts less so, but I hope to contribute small changes for the benefit those who live in the untold distant future.