I've just been on a 3 week trip to Japan and didn't see traditional Japanese dates used anywhere except on museum exhibits. Train tickets, bus tickets, hotel check-in / out dates, credit card receipts, tickets for various attractions etc. all displayed the date in ISO-8601 format.
It's interesting to ponder, but the traditional date format seems to have fallen out of use (probably with the advent of the computer era) and I genuinely don't think that this will be a problem.