For what it’s worth, Japan is not unique in using different calendars in different contexts.

There are several calendars in India, all based on the moon. In my state within India everyone uses the Gregorian calendar for most things except in certain cases. For example, no marriages happen during the month of Margazhi (December 15th - January 15th).

There’s no conspiracy in using a different calendar. It’s just a continuation of a cultural practice that hurts no one.