In the case of Japan, South Korea, and China, the richest and most developed parts of East Asia, they would rather deal with the effects of shrinking population than open up their countries to transformation via immigration. 
Also, people need to keep in the mind that just "opening up" the gates to immigration doesn't mean you will get the amount or type of immigrants you want. China has a bad human rights record and is not friendly to outsiders. There are much better places to go if you have an education and marketable skill.