My big assumption is that if a system cares about global timestamps, it should go all the way. If you have a “canonical system timestamp,” which I think is necessary, then you can operate on it functionally to get whatever local display that you need out of it. Your example with Country X means that dayOfWeek() AND dayOfMonth() are already both broken unless/until the language itself makes an emergency update to account for the change.
With dayOfMonth() I could substitute another function that handles the change. With dayOfWeek() I’d have to override the whole class, if possible.
I have seen this in action. A company I worked for was stuck with using outdated time libraries in Java because of IBM WebSphere (1.7? 1.8?). Those didn’t match the more recent libraries in Javascript (moment.js) and the differences caused significant problems, since the same locale keys had different time offsets.