Example: https://www.wikidata.org/wiki/Q20018609 contains (valid) qualifiers with "900 million years BCE Gregorian. In such cases the added "Gregorian" is almost totally pointless. It does not add any information that's useful. All you can learn from that is how the value is stored internally.
This is very similar to a TimeValue with precision month, where we do not show the day, even if it exists internally. Displaying it would not add useful information, only confusion.
I propose to almost revert the formatter back to how it was originally: Stop showing any calendar model indicator when the precision is so rough that it does not make a difference anyway. Originally the formatter did that starting from month precision. I think this was to early. Something that happened in 1499 Julian may have happened in 1500 Gregorian. I suggest to do that stating at precision 10 years (that's constant 8).