I think you and the others have perhaps confused borders with scarcity, and modeled humanity as purely economic in behavior, and culture as nothing more than a combination of aesthetics and economics.
Open borders isn’t actually the Good Guys. Having some limits on immigration isn’t actually The Forces of Evil. After all, if wanting to have a good, safe place to live that actually bothers to provide one with some support makes one evil, then economic migrants would themselves be evil.
Culture isn’t actually individual, nor are the engines that power economies. The dominance of some nations rather than others is tied up in history, but far from determined solely by war and exploitation.
Polygamy is actually bad. First (and second) cousin marriage are actually bad and have remained high in some ethnic communities, and in some countries. FGM happens even in first world nations when it’s allowed to enter, and it’s actually bad. Gays aren’t bad, but foreign ideologies, once dominant in a country, determine that country’s laws and will kill them, which is bad.
What’s necessary to deal with global poverty is to improve these foreign countries so that they are no longer net sources of immigrants. If you don’t, then no level of immigration will actually bring about the desired end in global poverty.
Their cultures will need to change, because only what is produced can be consumed, and cultures matter in determining production and consumption. Ambitious, high-IQ individuals will be necessary for this, and policies focusing on national development, education, and long-term investment.
Taking the immigrants is little more than a band-aid, and its effect would be erased by population growth.
There’s also one more matter. Open borders will, almost certainly, lead to a World Government. Then there will be nowhere to run. (The irony is not lost on me.)
Edit: To be honest you probably don’t actually want to argue this with me (which is why you didn’t), but out of all this I actually find the last point the most concerning.