Why is it not possible? The only "objective fact" is that people in certain areas in this country have lobbied hard to make sure that no one else should be able to move in anywhere around them. These rules are all reversible.
You can disagree with how we divvy up SF but claiming you should get to live there is in direct contradiction with the idea that everyone should get to live there.
Someone, somehow, will get bumped. You’re just advocating for a system that would put you there at the expense of someone else.