So you just keep adding new folks? That's my point, we need immigration, systematically, or our societies are dead.
There is also a dilution process by which you assimilate or adapt a population and if the % of new people is too high the culture that produced those societies basically disappears.
The last argument is empirically incorrect. Think of Vienna for example, most of the population there has roots from all over the Austrian Empire. Yet, it's distinctly Austrian.
It's not a given, it takes effort. But it can be done.