So, the the paper that you cited is based on one hell of an assumption. Because of the Costa Hawkins Act (1995), there has not been any new rent stabilized housing stock added in California in over 20 years. The Ellis Act (1985) makes it fairly easy for landlords in rent controlled jurisdictions to pull protected units off of the rental market. I find it hard to believe that rent control raises costs; it's more likely that the loss of affordable housing stock to the non-rental market, the incredibly high costs of building affordable housing in California, the relative lack of land in San Francisco, and institutional barriers to building have raised costs in SF.
In general, the "consensus" research from economics that proves rent control doesn't work, or causes gentrification, or is generally a bad thing is a lot less consensus than one might think. For example, the paper that you cite actually shows that rent control might be the only thing that has kept low income and elder San Francisco tenants in San Francisco!
Anti-rent control proponents usually position rent control as "the" solution to the housing crisis, as if it is an either/or proposition. In my mind, coupling rent control (tenant protections) with supply-side reforms (e.g., abolishing exclusionary zoning, upzoning SFH-zoned neighborhoods, etc.) is the only way to fix the housing crisis. I'm a "both/and" guy who thinks that you should use all tools at your disposal operating at multiple policy time horizons to fix a crisis of this magnitude.
