Rent control schemes don’t work like this, except in completely broken policies.

Landlords are given an allowance for rent control increases year over year. The point is that they basically have to take the maximum allowed every year to avoid getting stuck.

Rent control crushes supply to the degree that the rent control caps rents below the actual market rate.

If you're lucky enough to get rent controlled housing then you're in good shape. But good luck getting it when things get far enough down the timeline.

Rent fixing is the other side where supply is manipulated to extract the maximum profit. In this case the coordinated rent pricing action behaves like an oligopoly.

By legislating prices and price changes, the signal is muddied, and market participants cannot take action to match the movements of the supply and demand curves.

Prop 13’s property tax rate increase cap is also price fixing. These kinds of laws are mostly ways to enrich and reward those who got or were born somewhere first, and run counter to the vaunted meritocracy that a so called free market can encourage.

Edit: The most helpful thing the government can do is maximize price transparency, so the smaller entity can be on equal footing with the bigger entity about which way prices are moving. Tenant agreements should be public record, like land sales are, and that would not only help cops with kicking out squatters, but also give renters more power in negotiations.