(There's an actual open-borders advocate for you, by the way.)What is the optimal number of people to migrate from California to Massachusetts? No one knows. We find out through the market process. Potential migrants evaluate offers of employment, compare rents on apartments or prices of homes, and evaluate where they should live. When home prices go too high, or wages too low, people decide not to move. Whatever number do decide to move is roughly the optimal number.
The same should be true at the national level. Absent a market process, there is no way to centrally plan the optimal number and mix of immigrants any more than it was possible for the Soviet Union to centrally plan its markets. Instead of restricting labor flows at arbitrary places where politicians happened to draw lines on maps, we need a free market in labor. That means open borders. Not only would free immigration make the native-born population richer, but also it would be an effective way to help the poor of the world.
How much more should we be skeptical of government attempts to regulate a nation's culture?
And from a moral standpoint, I find it highly problematic to argue against others begin given opportunities that we would wish to have for ourselves.