OK here's a better alternative. Instead of rent control on a per-unit basis, cities could provide subsidies to long-term low-income residents that reduce their personal expenditure on rent. The subsidies would be paid for through taxes, thus amortizing the subsidy across the local tax base instead of impacting an individual landlord or unit.

But let me note that this must be done only for long-term residents (that is, those who have been there for years). For example, if someone moved to SF within the last 5 years, they should have known what the price of living there is. This is one of the most desirable cities, and it makes sense that it would be expensive and that not everyone would get to live there. Those moving there in recent years therefore, simply made an irresponsible personal choice and must yield to the consequences, rather than being subsidized at others' expense.