TOKYO—In announcing last week that Queen Elizabeth II died peacefully at age 96, Buckingham Palace didn’t give a cause.

It hasn’t been publicly disclosed whether the queen suffered from a particular fatal ailment, but the circumstances pointed to a debate that has been growing in Japan, one of the world’s most aged nations. When a very old person dies without any obvious trigger, should doctors try to come up with a cause? Or is it acceptable to say that the person died of old age?