>All it does is force land lords to massively increase rent amounts when someone moves out to account for multi-year market increases.

Depends on the scheme in place. There are a lot of places where the amount the landlord can raise the rent between tenants is capped.

There are two big problems with rent control: It results in a constriction of supply over time, and it causes degradation in housing stock quality. There's no reason to put one cent more into your rent controlled place than required by law.