Flack from whom, other than themselves?
First off, have you ever heard of colonialism? Europeans made incursions into those countries and regions much to the detriment of the indigeneous populations. Calling for more of what recalls negative memories (plundering, exploitation, raping, wanton slaughter) might not be what those former vassals wish for.
Chinese are IN Africa now, investing far more than the West is. Chinese interests are optimized to be one sided, however, so what infrastructure they build is maximized for extracting and transporting resources out. Chinese workers aren't allowed to fraternize with the locals to the point they bring their own food with them from China and aren't allowed to learn the language. They still prefer to be an insular society even as their reach broadens ever further. China is about business, not interference.
Japan? They're still around?
Central and South America HAS had Chinese and Japanese as long as the US has, MINUS the Asian Exclusion Act, so you might even see more. Cristobal Colon, colonization, Google.
Peru even had an ethnic (Peruvian born) Japanese President, Alberto Fujimori, back in the '90s. You might want to hit the Google switch on that one too.
There are Jewish communities and Welsh speaking communities going back generations all the way down in Argentina.
Now back to that pesky European colonial era thingy. Do you know why Britain has so many people from India, Jamaica, Nigeria and other countries whose coinage once featured British Monarchs? Go ahead, smart guy, take a guess.
France, with all those dandy folks from Le Algerie or Le Moroc, excuse me, Algeria and Morrocco?
German ties with the Ottoman Empire brought in Turks.
Russia's own current states brings in what ARE its own citizens, only more Asiatic. Sucks, I know. This is what happens when you stick your dick in someone else's pudding, buttercup.
In addition to allowing what basically were citizens of those former empires, there are other reasons, and not quite as altruistic as you think. See, there is no Mexico on the European southern border. The solution? Hungry-ish strong young men from, you guessed it, the now restive former provinces of now dead empires. So an influx of Moslems is not necessarily as altruistic as you rather pretend it to be.
The desire to replicate the US miracle is a MAJOR factor in importing foreigners, as that is STILL how our economy innovates and grows. Stop that, we become ossified, then die.