Ok I'll try to explain further.
YES "The Red Prince" gets the "Red Prince" tag which is unique to that background. Yet he also gets unique quests, he uncovers aspects of his past, and has NPCs specifically respond to his background.
As far as I understand, this is all linked to his trait/tag. If your character is tagged as a woman, you will potentially have access to a couple of quests unique to women, for example.
So I think what you want (and I want) is for them to create some tags for use by the custom character only that allow you to make the character more fun to play.
I expect that if they haven't done this yet, it's only because the game is still in Alpha.