To me it boils down to a game having interesting characters, regardless of their genre. Especially in story driven games that have a set cast of characters that the player cannot change or influence.
However, if the game is one where you create your own character (dark souls) or your character has a bare minimum of a background and the rest in all on you (Persona), then I think it's very important to have that option.
However, if the game is one where you create your own character (dark souls) or your character has a bare minimum of a background and the rest in all on you (Persona), then I think it's very important to have that option.