> I don't know if au jour d'aujourd'hui sounds horribly redundant in French

To me it does, it's irritating, like "to go up upstairs" (“monter en haut”). But most people evidently don't care, journalists do it all the time now.

I think it comes down to familiarity with expressions (or acronyms), as you explain. The more you internalize what a conjugate thing is, the more it becomes its own — and grammar be damned on the way, as logic evidently isn't the only path to understanding/speaking (perhaps not even the most common).