I liked the origins in DA:O--I didn't find it that restricting for my personal role play and I enjoyed their individual stories. That said, I don't think that format would work with bg3, given how many races and classes are available. I think having some quests tied to your background would work though and would be really cool. Similar to how it's handled in GW2 but perhaps less involved. If the quests were tied to one element of your character's background then it would provide some nice anchoring in the story while still giving the player freedom to determine their own backstory. For example, it could be tied to your background as a criminal, noble, soldier, or what have you. There's already small things tied to those backgrounds (such as the Baldurian dialogue options) that we didn't choose and were determined by race/background so having some quests tied to that wouldn't take away much more freedom.
That would be really cool, I hope they add some content related to your background.