If you have five people who want houses in place X, and there are four houses in place X, something has to give. The government could choose which of the five gets kicked out of place X (rent control does this, basically), the government could force the four houses be demolished and replaced with more, smaller houses (the character of place X would change, which probably no one wants), rents could rise until one person decides going to live somewhere else is their best option or two people decide being roommates is their best option. In none of these situations do the five people who want one of the four existing houses all get what they want.

If a popular, growing community has a plan for housing densification, but it’s going to take five years to build out, rent control is a reasonable bridge policy to keep the community together while the construction happens. But this idea that rent control can somehow by itself solve the underlying problem of not enough housing units in the places people want to live is a pipe dream.