(1) Since rent control laws put limits on increases (and not decreases) every landlord understands that he/she should test the upper boundary at all times to avoid renting severly below market rates during boom years. With sufficient landlords undertaking this task, rents should go higher than without this limitation. Moreover, the cost of moving is higher for the tenant (who has to find a home and move his/her property) than the landlord (who has to find a new tenant).
(2) real estate becomes less attractive builders and buyers, given the mandated constraints on charging rent. See https://web.stanford.edu/~diamondr/DMQ.pd. For a counter, see https://www.housinghumanright.org/wp-content/uploads/2018/11... (you'll have to wade through ad hominem attacks).
(3) high-income earners tend to benefit the most on rent control over time. As market rates for rentals increase (i.e., property up for rent), only higher-income individuals can afford to move in. Over time that leads to the displacement of lower-income individuals. Anecdotally, I can attest how some of my high-income earning friends pay very little for housing in SF because they locked in rates before 2011.
Lastly, pro-rent-control reports/papers I read highlighted the need for a comprehensive housing strategy beyond rent control, like increasing rental supply by making it easier to build ("It is also critical to recognize that the need for reforms extends beyond rent control and housing policy more broadly ... This includes developing new funding sources for affordable housing development and addressing exclusionary zoning policies at the root of the displacement crisis, https://haasinstitute.berkeley.edu/opening-door-rent-control). As the article already mentions, Scott Wiener's bill to override local zoning laws was shelved. The CA legislature did not have the stomach to address the underlying cause.
A far more sensible solution (IMO) is: (1) override zoning laws / ordinances that prohibit building more homes (2) tie rent control to income.