While I don’t disagree mixing of diverse people can be hard, I would simply point to American history as an example of how the empire you seem to laud was built by mixing peoples relentlessly. In fact immigrants tend to be the drivers of American growth, while the native born… not so much.
I find it fascinating you think culture doesn’t change with time, but with the mixing of different people into a culture only. What culture has been unchanged with time? Language itself mutates constantly, how can a culture be static with time? How does it stay static? The people in the culture change with every birth and every death, the memory of the culture is wiped out every 100 years. Written histories are a poor tool of continuity for something as complex as a culture. Human beings themselves change radically over the course of their lives. All things are impermanent, but human culture isn’t just impermanent, it’s an illusion.