There exist private sector mechanisms for enabling of migration from poor countries to rich countries. There also exist some government run mechanisms — visa lotteries in America for example — for facilitation of migration from poor countries to rich countries. I am in no way advocating that such mechanisms be scrapped. I myself am beneficiary of private sector mechanisms for facilitation of migration from poor to rich countries.
What I am saying is rich countries cannot via migration help poor countries become rich. Migration from poor countries to rich countries has to be based either on value propositions within private sectors, or on some paternalistic government led initiative. Migration must at end of the day be beneficial for rich countries, else it will generate resentment and anger within native populations of rich countries and backfire, e.g. Germany.
If rich countries want to help poor countries become richer, they must focus on strategies that induce leaders of poor countries to govern for their people, not for their own purses only. Many poor countries are poor only because of bad governance, not absence of resources. Making it difficult for bad leaders to spend most of their time outside of countries they refused to rule well is one way to induce leaders of poor countries to rule well. Note I never applied this policy to just anyone in poor countries, only past leaders who refused to rule for the interest of their people.
Migration, which brings the best and brightest from poor countries to rich countries, and which helps some of the downtrodden in poor countries to escape to rich countries always will have value, and must be encouraged. Neither of these initiatives are sustainable, however, if they are pursued to the disadvantage of people already domiciled in rich countries. Self interest of rich countries continues then to be important.
Migration never can be solution to helping poor countries become rich.