What do you mean, what knowing the day of week a date is useful for ?

Yes, that's what people typically use a calendar for. So you agree that this trick isn't useful for anything?

I'm reminded of the scene in Back To The Future II in which people in the 19th century scoffed that someday someone might "run for fun" despite the ubiquity of motorized transportation.

"3 Nov" is ambiguous, it could mean 2020-11-03 or 2021-11-03, or any other year. And by the way, "3 Nov 21" is also ambiguous, it could be 2021-11-03 or 1921-11-03. Lots of stuff happened in 1921.

Also, "3 Nov 21" works only as long as everyone speaks a language in which "Nov" actually stands for November. Abbreviations can have false friends in some languages. It's the reason most EU personal documents try to avoid using text as much as possible because it's impractical to write it in 20+ languages.