Premise I can't stop thinking about but don't know how to write

I've been sitting on this for months and I think I need to just throw it into the room because I can't figure out the story myself. The premise: a city that has completely solved its housing crisis - there is housing for everyone, it's affordable, it's well-designed. The catch: the housing algorithm assigns your home based on psychological profiling. You don't choose where you live; the system places you where it has calculated you will thrive. Most people are happy with their placement. The system is, statistically, correct. The city's mental health metrics are the best in the world. The story I want to tell is about the people who are incorrectly placed. Not people who think they're incorrectly placed and turn out to be wrong (that's the easy version). People who are genuinely in the wrong home and can prove it, and the system still won't move them, because the system's error rate is 2% and there is no appeals process for a 2% error rate when it's saving thousands of people. I know the theme (systemic correctness vs individual justice). I don't know the genre, the format, or the protagonist. Thoughts?