Why would there be anything wrong with it? This is the way cultures and people have changed since time immemorial.
Yeah, because some empire came and killed your people off and conquered your lands and enslaved your survivors and erased your culture so they could replace it their own.
Not because people wiped themselves off the map because they wouldn't have children.
No culture is "erased" as a result of this. Even if Japan fails to have children, Japanese culture and the Japanese nation will continue. It will look different, certainly. But there's nothing magical or better about the way things used to be simply because they used to be that way. Change is inevitable, and more than that, it is good.
No. Nations are a collection of people with shared ethnicity, land, culture, language, history. If the japanese people disappear, the nation will also disappear. It's not going to magically continue just because the country of Japan is still there. Can't have a nation without its people.
Japan will exist as long as people live there and call it Japan. It has nothing to do with ethnicity, land, culture, or history.
> nation
> A people who share common customs, origins, history, and frequently language
There are nations without states. There are also nation states. The latter is more precise than country which does not imply any dominant ethnic group.
Doesn't change the fact birth rates in Japan are below replacement. Am I missing something here?