The whole character customizer is completely pointless, since:
(a) there's no third person view option
(b) your character doesn't show a reflection, even in surfaces where NPCs are showing a reflection
(c) some if not all of the cutscenes don't show your character either
(d) none of it matters anyways in-game.
Character customization is extremely important for lots of people - no matter if they can look at their character or not.
Appearance for many is as vital to make a character "their own" as the stat & skill customization is.
You can't just handwave that away.
Of course, you are still correct that you should at least be able to look at yourself in this game and that you can't is just one of the many shortcomings of it.
Working mirrors are really not that impossible to have in a game.
It's just a another camera looking through from the "other side" of the mirror, with its view projected onto the mirror surface. Not totally trivial, but you'd think a game of that scale should pull it off.