Character backgrounds have varied from game to game. In BG/2 you start with very minimal information about your past, learn more as you go along, and determine who you will become. But you don't CHOOSE elements of your background.

In the Witcher series, again due to memory issues, you only know part of your background to start, learn more as you progress, and again decide over time what kind of person you will become.

Torment started you off as a blank slate, and again you learned your history as you progressed.

On the other hand, newer games such as PoE1 and Tyranny allowed you to select some aspects of your history and let you more fully develop as you go along.

I think BG3 could offer some "general" background options (family alive? dead?, religious choice?, goals - money, power, romance-) and perhaps offer you some opportunities to advance and develop these traits through additional conversation or quest options, but that admittedly would take quite a bit of work to do in any meaningful way, and would STILL have to be limited to a handful of background options - more than that and you start hitting the level of oprions in a game like Disco Elysium, and that would require building an entire sub-game within the game.

And it would only work in custom characters you 'roll up'. Origin characters should be limited to the prescribed background and motivations they were specifically built for. You should NOT expect to be able to play Asterion as a misunderstood, bard wanna be, or Shadow as a spy for Selune, attempting to learn what Shar us up to, just because you feel like it, with different backgrounds selected at start up.