I also find this very odd. In many trips to various parts of Japan, I have never, ever been approached by police. In fact, the only times I have ever spoken with police officers was when I went to the koban seeking directions. I am really curious as to what there is in your appearance, dress, demeanor or locations you visit that is triggering their profiles.
As to the passport, why do you not have it in your possession as is required? That is just asking for trouble, regardless of what country you are visiting.
JR