I suppose they could be flown out of the country to be buried in another country... better save your Yen!!!
Not to be difficult, but there is a strong Japanese custom of the 'family' village/hometown/burial place. There is a festival in the Summer "O-Bon" where the family that has passed on is remembered, and welcomed back for a visit, similar to the Day of the Dead in Mexico. There are markers that are still tended and prayed at after centuries I'm told. I can tell you that William Adams' grave is still marked and remembered as are those of other non-Japanese. How much more so are the places ones parents and grandparents and perhaps children are buried.
It is easy to say "just fly them to another county to bury" but what are some of the things that entails? First finding a country that is willing to take a foreigner for burial. Next, the cost could be prohibitive. Then there's the idea of not being able to visit the grave, to pay respects, to tend it as is the custom; how would they know if it would be treated with respect by strangers?
Also, the tradition of cremation in Japan is Very Old. The Heian period literature has many instances of deaths and cremation and mourning customs. It is not just a matter of not much room though that is part of it now. There is only so much land on the islands and much of it is needed for the living to inhabit and work and grow food while other parts are not really habitable.