It’s possible to do much more though in terms of giving your character a backstory in a CRPG though.
As an example, Dragon Age Origins had a different solo mission at the beginning of the game for almost each race/class combination, and the choices and relationships you develop during those missions can come up in the main story.
As another example, Tyranny started the character creation process with a brief text-based choose-your-own-adventure story. The choices you made there not only influenced stuff that happened to you throughout the story, it also affected your starting relationship with certain factions.
Edit: like what if they did a small backstory mission depending on the background/class you picked which ended when the nautilus appeared and abducted Tav? That would be great and would make the city of Baldur’s Gate feel more like home, which it’s meant to.