I believe you might be thinking of month-to-month, which is not a traditional lease. On all fixed term leases over a month rent cannot be changed during the term of the lease.

If you have a lot of money and you want to build/buy a rental property, would you do it in a) a growing city with no rent control where your discounted future cash flows are unbounded or b) a city where there is a law placing a ceiling on your returns.

All else being equal, you are going to choose the city without rent control to build your new housing units in (or invest in something other than real estate altogether), thus illustrating how rent control disincentives new investment in housing, and specifically low-income rental housing.