Set backgrounds do very much go against the whole free character choice. The goal of CP77 seemed to me based on what I've read, that you can make any sort of character you want that fits in the world. Alley thugs, street hookers, budding celebrity, whatever.
What might be good is to look at Mount and Blade rather than Dragon Age, where their character creation is very RPG-ish in how you outline your own background. Choose things such as sex, social standing, events in your past, and motivations.
If we're to have a Background mechanic, I'd want it to be very free. Instead of picking x, y, or z, you pick from a myriad of different elements to piece together your own background for your own personal character, which can effect where the game starts you off by default. Then having a selection screen where you can tweak all these default values (With an option to skip the RPG-Story-fluff-ness to go straight to that screen, which many would appreciate I imagine.)
Yeah that works too.
If they can't take inspirations from DAO just use M&B.