DragonAge:Origins showed that it was possible to offer a number of different background stories, but each of them still resolved to being conscripted as a Grey Warden, and thereafter following a singular path. Your request would be the equivalent in DA:O of being able to choose NOT to join the Grey Wardens, and do something else instead, leading to a very different storyline. Bioware actually did provide a single alternative narrative as DLC, but only for a small part of the game ( the Darkspawn Chronicles ).
BG3 seems to be actually intent on offering ( at least ) two completely different, but interlinked, story paths, which, if it leads through to multiple different resolutions and outcomes is a step away from the cinematic story norm.
Even with this, fairly limited, dynamic content, the conversation trees in BG3 are already struggling ( and failing ) to honour the played experience; and that's with the player and all companions linked through the Tadpole story thread.
With the way games are currently made ( static, pre-determined content ), I doubt the experience you would like is really practical.
