If every apartment in a region is required to be cheap, then there is no value for the landlord in trying to be tricky. If some apartments are cheap and some and expensive, there is value for the landlord in trying to turn cheap apartments into expensive apartments, possibly by driving out the current tenants to get around the rent control laws.
If there are few apartments on the market because some people do move and high demand those apartments will fetch high prices.
If there are few apartments on the market because some people do move and high demand those apartments will fetch high prices.