See this alot among the Amish/Anabaptists here in the United States. There's no more farmland to be bought in the places they live, so each generation has the farm split between 4 and 6 sons, and they keep getting tinier. Until, at some point, it can no longer be divided. Moving and setting up a new colony elsewhere is difficult in the extreme, so it usually happens far past the point that it would make sense to split them (down to just a couple of hectares in many cases).
Sometimes when it's at its most extreme, they'll all take their pooled savings and go buy a square kilometer or two out west, but there aren't so many places like that left to buy, especially that are worth farming.
> So if countries like Japan want to attract immigration from here,
Here's another funny one about Japan. There is a not-well-known but peculiar class of potential immigrants. After (before?) a bunch of Japanese emigrated to Brazil. But, being Japanese, they didn't give up speaking Japanese. So they're more or less fully ethnically Japanese, speak the language as their first language, etc. And, as it turns out, many of them would be willing to move back to the land of their grandparents and great grandparents, if there were jobs.
Also, there are jobs!
So, the government initially sets up a program welcoming them back. But it turns out that they aren't welcome, either by elements in their own government, or society at large. They're simply too alien. Eventually, someone gets voted out, or retires out of government, the program is shut down, and those returnees are forced to go back to Brazil.
If Japanese society thinks those people are too alien, too foreign, to fit in... what chance do the Vietnamese have?