Rent controls only really hurt a specific section of landlords.
Those with low rents, and who want less churn in tenants. Long term landlords. Those with low margins.
The shortage from PRZ is actually to the advantage to new landlords, and bigger yield (high rents), and mobile. (can buy and sell)
Also those with finance to do extensive refurbishments.
So it mainly discourages, low rents, and encourages renting to the high end of the market.
The majority of new rentals are at the top end of the market. The minority is at the low end.
No shortage at the top end of the market if you have the funds.
So not only does it effect supply. It further reduces supply where the country needs it most, and creates supply where its needed least.
Its probably reflects the growing disparity in wealth, thats also happening. Which is a reversal of social trends in the last century.
That said this is particular to how RPZ have been implemented here. They aren't always done the same way.
Though they do tend to have same end result overall.