This is clearly the wrong way to think about it. Dates forward and backward from this flag date exist in both calendars and it's straightforward to convert between them.
Such a flag day didn't involve removing days from one calendar or the other, it switched between them.
The way I imagine it is like the calendars are both rulers that are slightly off from each other. We were using one ruler, and at a certain point we went from using one to the other, so our "present" was never mapped to those dates. But you can represent any point in time as any of those calendars, like we can represent a specific temperature as Fahrenheit or Celsius. The calendars extend forwards and backwards to infinity.
I would think of it as Calendar A uses Calandar B until time point T and then uses Calendar C. These dates exist in Calendars B and C, but do not exist in Calendar A.
It's not a wrong way to think about it. There are some use cases for proleptic calendars, but there are just as many where it's completely inappropriate. If you ever need to compare what day you think it is with what day someone in the past thought it was, then yes those dates don't exist in any real sense.
I wouldn't say it's it's straightforward to convert between them, either. The Gregorian calendar was first adopted in 1582, but the UK and it's colonies didn't follow suit until 1752. Russia didn't convert until 1918, and Greece didn't switch until 1923. We're just over 100 years out from active use of the Julian calendar. So you have to know who the speaker is and where they are or where they are from to know what they mean.
Since these places switched at different times, they had to skip a different number of days. It was 10 in the 16th century. It was 13 in the 20th!
If you're reading a journal by a British man who lived in Russia through the end of the Great War and then moved to Greece in 1920, what does he mean when he's talking about a lunar eclipse he just witnessed?
I would say it's almost never appropriate unless you're directly quoting source texts.
If you are talking about a historical event from Egypt in 500 BCE, you would say "this happened in 500 BCE", not "this happened in year 26 of the 27th dynasty".
The distinction is important in the context of doing historical research, but it is no more appropriate to write dates in secondary sources using the Julian calendar than it would be to try to explain Egyptian history by spouting hieroglyphics at people.
Yeah, but how often are we talking about exactly specific dates without referring to specific historical texts?
The Magna Carta was sealed on June 15, 1215 for the Julian calendar. But if you want the actual anniversary, it was sealed on June 22, 1215 using the proleptic Gregorian calendar. Do you want to know the date people remember, ir the date of the true anniversary?
The coronation of Henry VIII is listed almost everywhere you look as June 24, 1509. Except that's also Julian. The date of the Gregorian calendar is July 4, 1509.
We don't remember the proleptic dates. We remember the dates that were then in use.
And if you say you're just always going to use the contemporary recorded date, that's fine. Until you get to dates like February 29, 1700. What do you put in your system then?