In bigger european cities gets to wierd situations because investors buy houses/flats as investment and know that they will make big $$$ just over time as the price of the flat increases. Renting it out is work, flat gets used (looses value) and whats worse if you (and all other investors) keep it empty you increase prices of rent/property everywher. In other words you might hurt your investment. So people keep it empty or set insanely high rent prices exploiting the desperate people looking for anything.
Its crazy how many empty flats around me there are yet we are in “housing crisis”.
Instead of price control first regulation we would need is not allow empty flats just laying there. Also we should accept that housing is human right and not allow it to be tool to exploit masses. So stop home speculation by for example progresively more taxing owning every home after the first one. Companies that own/manage rentals should be under extra scrutiny just like energy/water companies are. Having safe space to sleep is as much human right/need as access to water.