Rent control doesn't work in the long run.
Sweden has had rent control since the 1940's, and as a result the rental housing market is completely dysfunctional by international standards.
In Stockholm, demand for central inner city apartments is way, way, way higher than supply. The rationing method used is a queue administered by the city, and the queue time for the most sought-after areas is on average 17 years. Even the most remote areas have a queue-time of at least a year.
SEVENTEEN YEARS. GOOD LUCK, COMRADE.
This means that if you want to move to Stockholm from outside the city or outside the country, you will not get a rental apartment, unless you rent one second-hand or third-hand, unless you buy a rental apartment under the table, unless you have "contacts", or unless you buy a condo on the perfectly functional condo market.
Since there's a functioning market for condos, but a dysfunctional market for rental complexes, the ROI on building a condo complex is decent, but the ROI on building a rental complex is abysmal. You're better off setting your pile of money on fire than invest in building rental apartments. No private for-profit company will voluntarily build new rental apartments. So the only actors left that could do that is the city itself. However, the city government changes politically every four years, and even if there's a left-wing majority, there is absolutely no budget to increase supply meaningfully.
In addition, there's political and economical pressure to convert the city's housing stock to condos. Current renters love it, because it means they can realize the value of their rental into cold hard cash, and the city council loves it because they get a temporary cash infusion. It's zero-sum for the housing stock, and the long-term effects are shit, because the rental supply diminishes, making the queues worse.
The net result is that it is incredibly hard for companies to attract outside talent, because finding a place to live if you don't already live in Stockholm, is incredibly hard. If you're a transient worker or simply doesn't want to buy an apartment, and if you don't have a decade of accumulated queue time, you have to rent from the much more expensive second-hand weird market, which means that companies have to pay you much more than they would have to pay a local for the same job.
Compare this with SF, or any other large city with a functional housing market, where every company has to pay their employees a wage that covers the housing market rate, which means that there's no difference between local workers and outside workers, and it means that the city has a much easier time attracting new people who want to come there and live there. Because anyone can live there, if they just show up with enough cash to pay the market rate.
Yes, market rates means you get a host of problems, gentrification most of them, but that's a positive problem compared to all the horrible problems that rent control bring.