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Japan also has a distinctly Japanese culture that it's aging population desperately wants to cling to.
So Japanese factories are filled with Filipino immigrants who are underpaid and overworked and the elderly are cared for by Filipino nurses who are drastically underpaid for their labor. The Phillipines are becoming to Japan what Mexico is to the US. And they house those workers in company provided housing, where they interact less with the general population. And the last thing old people want is to see immigrants "taking over" by moving into the communities and ruining it with their differences. Hence why it's completely legal to engage in housing discrimination against immigrants. 
Meanwhile, the government still publicly maintains the appearance of strict immigration requirements while under the radar servicing this kind of arrangement. 
The future of Japan is blique. The elderly are utterly dominant as a political force and their interests supplant all others. There is also a thoroughly entrenched risk-averse business culture that stifles innovation and drains all the life out of younger generations. 
What Japan has in its favor is that the same stifling bureaucracy that limits innovation and sucks the life out of younger generations is also highly self perpetuating. The country won't collapse in any rush, but it's institutions will feel extreme strain as there simply will not be enough people producing wealth to sustain all those consuming it.
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. >

I’ll add that Japan and South Korea are in a unique situation. Based on geography, they can actually do a fairly strict and efficient job of controlling what type of immigrants are brought into their countries. They have total control of their borders, the fact that there are no easy land routes for immigration is a plus when it comes to this issue. So if they are serious about starting to ease immigration rules, they could probably do a much better job than the west in that regard. Of course your gonna have people overstay their visas and try and carve out a life under the radar but then the homogeneity of their respective countries would make that much harder for “foreigners”. It really is new territory for a lot of these countries and I hope they take a long hard look at other western countries to try and figure out a comprehensive immigration/labor plan that is beneficial for bother the immigrant and the host country