All that's needed is that new immigrants should do significantly better than they did in their home country, do some good in the country they've moved to.
Notice that your two assumptions nearly contradict each other. After all if the average citizen of the old country was as capable of doing good as the average citizen of the destination, the old country wouldn't be the kind of place one needs to leave to do significantly better.
Consider the common case of a Latin American man who leaves to become a construction worker in the US.
He's a basically sensible person who's willing to work hard, but due to corruption, lack of infrastructure, and probably prejudice in Latin America, he's extremely poor.
He risks his life to go to America, where he's still subject to corruption (employers can get away with cheating him of his wages, and there may be payments for his work into Social Security that he will almost certainly never be able to collect) and prejudice, but he's still better off because he's hooked into much better infrastructure, probably less corruption, and possibly less prejudice.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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