Can't someone in Japan collect a copy of my family registry for me?
It's a reasonable option that seems to have worked for a few out there. If the person whom you've asked to collect your koseki registry is a professional genealogist, or you've given somebody in Japan the authority to be something akin to your power of attorney in regard to this matter, yes, they might be able to collect copies of your records for you.
Before asking a Japanese pen or e-mail pal to go to a city hall and attempt to collect your family registry however, please consider that such a request may be placing them in a difficult situation. While they may sincerely want to help you, the folks at city hall may prohibit your pal from gaining access to your family registry without the proper legal documents from you. If you do manage to find a very dear soul who is willing to wade through the formidable tide of Japanese bureaucracy, please realize what a gem of a pal you've found. These records are considered highly personal by many Japanese.
Koseki records are not held library style where one may gain access to the records by simply entering the appropriate room. Since they are held and protected by city hall, only city employees are allowed access to these records. A researcher must therefore fill out the appropriate request form, wait in line to submit the form, and wait in line to receive the information. In larger city halls this could possibly be a time consuming process.