I agree, because once you have moved and not just within a city but across national borders, a home coordinate makes no sense at all (especially in terms of distance and directions). If you leave the old home coordinate, all new caches found are wrong in the statistics, and if you change the home coordinate to the new coordinate, all old caches found consume the statistics.
In addition to one (or more) home coordinates, it should of course also be possible to enter a date from which this coordinate is valid.
Since the PGC team has often been asked for this, I unfortunately already know the answer ... You do not have access to the user's home coordinate and therefore cannot implement it.