Being treated like an outsider everywhere, by everyone, bothers me too, but the problem with adding this retroactively is it's very likely to clash with the backgrounds players have already invented for their characters.
Not to mention that it’s not necessarily inherent that someone looking at you will know where you’re from. How would a Dunmer look at another Dunmer and instantly know they’re from Vvardenfell? It should be a dialogue choice IMO. That way, people from weird places (or just flat out liars) still get covered.