It's possible to become a Japanese citizen, just very difficult. Arudo Debito became a Japanese citizen.
Yeah. There's also some Finnish guy who became a citizen, and he's in the Diet. And didn't Ruru (formerly of T&C Bomber) become a citizen, hence her surname Honda?
So it is, in fact, possible to become a Japanese citizen, however it is kind of doinky because you can't have dual citizenship. I think that if they did allow dual citizenship, there would probably be more gaijin becoming citizens.
Also, there are immigrants - mostly other Asians, particularly Chinese, but also some people from Brazil and some other Latin American countries. There are several smaller towns with large Brazilian communities. Though there are not as many immigrants as in Western countries, immigration isn't forbidden.