I'm all in favor of the intentions behind rent control, but the implementation is an atrocious way to achieving its goals. If the goal is to help the poor long-time residents of a city, then do that directly. Raise property taxes, impose a city-income-tax, and use the proceeds to offer assistance to means-tested long-time residents. This would be far better than what SF has currently.
And effective rent would require controlling evictions and controlling rents on vacant units (infringing further on sacred property rights, certainly).
Now, the most effective policy would involved rent control but with exemptions for new very high density units, incentivizing increases in the total housing stock for an urban area.
But we're here with weak rent control and tacit collusion of homeowners and builders, who talk about their property rights when convenient and use the state to keep their monopoly when convenient.
Your hypothetical disadvantaged woman would have zero ability to pay $2000/month rent for a studio, however many of these might be available. She would likely find it hard to get an apartment in a rent-controlled situation - so the situation is effectively "hard versus impossible", a condition where "hard" is less harsh.
And I mean, I've lived off and on in the Bay Area under both these conditions over the last forty years and the impossible rents of course are the hardest for those of lesser means. Of frickin course.