Regulating big rent increases for existing tenants isn't a bad economic policy if you compensate through other means ( e.g. you ensure there's a path to homeownership for those tenants, so they don't stay forever, and that new housing stock for affordable rent is added frequently).

In France there's a maximum amount you can increase a tenant's rent with, defined yearly based on market prices. Combined with one of the most popular investment vehicles, which is a buy new ( thus incentivising construction) to rent (at defined affordable prices) programme which gets you tax breaks for 10 years, and after that most people usually sell. Alongside that cities are mandated by law to have a certain percentage of "social"(affordable) housing available, so when private construction adds housing stock, cities have to add on top of it. That helps keep renting affordable while also making sure new construction appears.