Two Amsterdam tenants had great success in reporting their landlord to the Huurcommissie rent tribunal for charging them exorbitant rent. The Huurcommissie ordered the landlord to lower the rent for a small, leaky, drafty room on Keizersgracht from 1,950 euros to temporarily 95 euros per month. The rent for another room in the same building was lowered from 1,200 euros to temporarily 93 euros.
For people to build or buy their own homes they need to be able to afford them. They can’t, which is why they rent. If landlords don’t offer flats for rent anymore, people don’t magically have more money to buy or build.
Corporation and private investors build rental properties because they aim to profit from them, and if that isn’t the case anymore, their construction activity slows down and then stops. As can currently be seen e.g. in Germany.
The only way to effectively counter rising rents in cities is public, non profit construction and decentralization efforts (so people don’t all flock to the few places that are hip to live in).