This whole line of reasoning can also be used to argue that there is no such thing as culture: neither "French culture", or "English culture", or "New York cult

This whole line of reasoning can also be used to argue that there is no such thing as culture: neither "French culture", or "English culture", or "New York culture", or "Florida culture", etc. exist. Also, population mixing and movements across time doesn't preclude the existence of more or less distinguishable groups inside the said population.