In the case of BG1 the said background is what happens with the charname along with the mystery that surrounds him. It is particularly cool that you can experience all the story yourself both embracing his ancestry and writing your own story. No wonder for me why so many people being attracted to him. There’s no need to force any cause for their company, since the charname himself is a cause enough.
This is what BG3 lacks imo. Mainchar is bland and practically non existent. He resembles more of an observer, while the first roles belong to his companions.
Companions in BG1 don't care about your character's mystery; you don't discuss the magical dreams or the random assassin attacks, or Gorion's letter with them. Even with those that should care, e.g. Dynaheir, since she is supposedly there to figure out the prophecy. You don't get to write your own story in BG1 either. The main plot follows the same route to arrive at the one possible ending (other being losing the game). Whether you played a hero or a villain, whether your character was wise and noble, or dumber than a rock and with the charisma of a slug, none of this matters. The story in BG1 doesn't care about the character you have created. There is very little character reactivity in BG2, and while the main plot has some branching, ultimately it doesn't impact the ending either. ToB is the first one in the series to give you a choice of the ending, but this yes/no question is available to all generalist charnames to complete the BG saga.
Compare that to a game that came out close to BG1 (if I remember things right): Planescape Torment. How the story unfolds and ends depends on the Nameless One you are playing. That is how writing your character's story in a game looks like.