Because culture is not an abstract set of ideas separate from its people. You can only adopt a culture you weren't brought up in to a certain degree, and usually very shallowly.
There have been non-ethnically Yamato people in Japan for at least centuries. However Japanese society or law might have treated them, are you saying the Zainichi are culturally less Japanese than ethnic Japanese?
Seems like a lack of faith in societies to properly integrate new arrivals.
Why assume modern day East Asian countries will integrate new arrivals the same way as European and North American nations do?
And are you aware that international migration has been happening for millennia? All nations have people who have assimilated and integrated, to different degrees.
Most unique cultures are likely to have disappeared by force via conquest and colonization, not through voluntary migration. And in most cases, it is the migrants themselves' cultures that get lost in favor of the host nation's culture.
