I find these things so much easier to think about if you consider the change as a change from one calendar system to another calendar system. Those 10 days certainly exist, in both calendar systems, they just represent different points in time. I.e., I think it's easier to just consider both calendar systems as the rules, extended forward & backwards infinitely ("proleptic"). Some people switched from a Julian calendar to a Gregorian one in 1582.

"Some people did not experience days with these labels in some areas of the world" … I get where it's coming from, but it's not how I'd build a library.

If you worry about the switch, then you have to ask "which switch?" which TFA only lightly touches on. The 1582 one is famous, of course, but not everyone switched, and other parts of the worlds switched as time went on, to as late as 1918, when Russia switched.[1] (And you can see other messiness in that table, too.)

Needing to deal with it is niche enough that I think most language std libs should implement the proleptic Gregorian calendar, and let an application whose niche requires it deal with the switch (& whichever switch it requires).

[1] https://en.wikipedia.org/wiki/List_of_adoption_dates_of_the_...