When I was living in Japan I always had to "romanize" my Japanese address if I got something shipped from USA because USPS only allows ASCII. Even if this did create problems locally - post always arrive quicker (in my experience) if the address is in proper Japanese. When I got mail from my home country I got it forwarded via my company and they always just stuck on a printed label with my address, in Kanji. No problems there. Worked fine for years.
However, my home country postal system has since changed to an online system for sending post out of the country: You go to a website and enter the destination address, then you pay and it'll print a code which you just give to the actual post office when you bring the letter/package whatever. What's infuriating is that they don't allow Japanese addresses - I can enter it, but it just creates an error message. So I again have to come up with a crude romanized address and cross fingers that it'll arrive (which it usually does - but up to a few weeks delayed).
In short - things are not getting betters over the years.