Japan is anti-immigration and they are rich. And that's despite them being in the Western block with defining pro-immigration ideology. The same is true for South Korea.
Both Japan and Korea have around 7 times fewer immigrants as a percentage of the population than major countries in the EU and the US.
Therefore, I see even less of a chance for China, which is not under the Western block, to accept any kind of mass immigration in the future, basically 0 chance. I'm not including overseas Chinese returning, high net-worth individuals, or other specialized programs.
We can talk about selective, high-quality immigration of educated and intelligent immigrants, but that's not many people.
And also China has no problem with creating a high-quality productive and educated population from its own base in tremendous numbers.
When you say East Asian, I typically associate it only with China, Japan, and Korea, and they are very close culturally and genetically. (Also all 3 are historically very closed societies due to their geographies).
Therefore, if under Western pressure Japan and South Korea are anti-immigration, then it's logical to assume that China is even more so that.
China was never a closed society. We didn't go from small bronze age tribes along the Yellow River to a continent spanning empire by being closed off. Our culture did not spread from China to the furthest reaches of Central Asia and tropical Vietnam by being closed off.
China's geography is closed on 2 sides, but open to the north, particularly the northwest, and connected with Indian Ocean trade to the south. We ruled an empire, so did Persia and Rome, we could not afford to be closed off. We sent envoys to India and Persia in 100 BC and Japan in 200 AD. Expensive missions with the main purpose of exploration and learning. We tried to reach Rome but were tricked by the Persians. We traded with Arabia via sea. Closed off? Meanwhile Japan and Korea were hanging people for talking with foreigners.
Korea was known as the hermit kingdom, but nobody ever said China was the hermit empire.
For today:
Japan and South Korea are not rich enough
for the hard work necessary to integrate to attract immigrants.
Example: South Korea is legally very open to immigration. They've been trying to attract immigrants.
You just have to learn Korean, the language furthest from indo European languages that 50% of the world speaks - further than even Chinese. Korean does not even have the same sentence structure as indo European languages and the language changes depending on the relative social position because of honorifics. You have to learn it well enough to live there for 5 years while employed by a Korean company.
Then you and all your children have to agree to be conscripted for 2 years in your youth, to fight in case of apocalyptic nuclear WW3.
Then you have to accept that your children will be working as hard as they would in a 3rd world country in school.
You know how Indians talk about how they lose sleep and cram for JEE tests for IIT? That's everyone in South Korea.
And for all that, you get paid 3k USD a month while paying developed country prices.
An IT professional in India can get paid 10-15k USD while paying Indian prices.
that's not hourly. Koreans work some of the longest hours in the world.
and 50% of Koreans attend university so what usually gets someone in the door in the west is just normal in South Korea.