When rent control happens, it motivates people in controlled housing to STAY there, even if their needs change (ie, their job moves, they have more or fewer people in family now, etc) because they can't get as cheap a rent elsewhere. This means that the people who get into the price-controlled housing no longer respond to market pressure.
Generally, rent control regulations do NOT cover "luxury" housing, so the effect of rent control is to drive builders to make more expensive units, rather than lower-cost units, because they can charge profitable rents--and retain control of when and how they change rents--in luxury units. Building (or buying or renovating) low-rent units when the government controls what you can charge is a recipe for going broke. New York City has had many buildings literally abandoned by their owners because the rents allowed did not cover the cost of maintenance, renovation, etc. These buildings become slums, then squatter housing, then derelicts...
Seattle has a rental housing shortage laregly because the city forbids buying several adjacent houses and putting a small multi-unit rental complex on it. So there are miles of little old 40's and 50's houses with bad plumbing, poor insulation, large, eco-hostile yards, etc...owned by older couples who can't really maintain them. But since builders can't turn them into useable rental properties, there's not enough demand for them to make it worthwhile for the owners to sell. (And the cost of renovation is pretty large for a single family to afford.) If they permitted low-rise (3 story or less), limited-unit apartment structures, Seattle housing costs would drop dramatically within 6 years. But I'm not expecting there to be any change in my lifetime.
People think "Landlords" are these cartoon millionaires with limosines and diamonds, when most landlords are individuals that own a few buildings and are trying to fund their own retirement out of the proceeds. Villifying "the landlords" is a way to buy votes--but not to solve a housing crisis. Speeding up permitting processes, allowing limited multi-family dwellings in single-family neighborhoods, and legislating *against* rent control would help--but that's not going to happen. Logic is not the strong suit of voters, nor of politicians.
Just my thoughts, MK