They won't because of their concept of origin characters.
Origin characters HAVE to have the same story as custom characters.... But they can also have side story.
There's no reason a custom character can't be as cool as an origin. Through dialogue options, we could pick an aspect of our background that is not class or race specific. For instance, you have a mission to to hunt down X item or person. Or maybe you want to redeem the name of your family/organization. Those are two easy examples that could have custom origin quests and stories that would fit any race/class combo.
Let the player choose from 2 or 3 possible backgrounds/motivations, then write some story and quests that tie into that.
P.S. Give a reason why the PC is the group leader. Currently the companions all have compelling reasons to be the party leader, but they follow you instead because the game told them to. This needs to be addressed, and custom origins would be a great place to insert that.