If you freely choose where to live, that means you get (at least) $3000 of value renting a $3000/month apartment no matter where you rent it. If it's more expensive for the same size of unit in one place or another, that means you're paying for amenities, or a short commute, or access to a particular job market. So giving people more money to live in SF would be subsidizing the consumption of the amenities that SF provides, or to put it less delicately, you're rewarding San Francisco residents just for living there. One could potentially argue that the subsidy is warranted, but generally I am skeptical that such a subsidy would be welfare enhancing. My suspicion is it would just cause people to overconsume San Francisco real estate relative to their latent preferences.
"My suspicion is it would just cause people to overconsume San Francisco real estate relative to their latent preferences."
Which seems like it would make the situation worse, long term. We can increase density further, but there's a limited amount of SF to go around, so driving overconsumption would raise prices, and then we'd need to raise the subsidy we give SF further.
