Ahh, in that case, Larian could just set aside several different homes in different areas of the city as you suggested. Depending on which background the player chose would determine which home would belong to the player. The other homes would just be abandoned structures that could be investigated and plundered should you find them. This doesn't have to be all that complicated. Someone with an urchin background would likely live in a flophouse type structure, the noble would live on the outskirts of the noble area, the artisan in the mercantile section, etc. Even BG1 had enough random buildings to have pulled that off should the player character have originated in Baldurs Gate. Sure, it means that Larian would have to create a backstory for each location, and have only one backstory instance in each play trough depending on what background was chosen, but it may be the best answer to the problem. I don't think they should create NPCs to generate quests or family/friends to sidetrack th player with drama that isn't neccessary though. The noble section you might find a note to Tav suggesting that the family relocated to Waterdeep temporarily until things settled down, the artisan district you might find from a neighbor that the merchant you worked for had joined a caravan to Amn and wasn't expected back in the near future, the urchin could just be give the rough side of the flop house matrons tongue and told in no uncertain terms he was no longer welcome after missing all that rent and that his bed was already occupied.
That is the solution, do I really think that Larian will bother? No, not really.