Landlords in supply-constrained cities are able to charge the maximum rent their tenants can afford; and increase in landlord costs is thus not able to be passed onto the tenant, because if the tenant could bear more they would already be charged that much.

This is in aggregate, of course; individual landlords may charge less than what individual tenants can bear but across the rental market, landlords extract monopoly rents already.

That's why you will find rents increase proportionately to incomes, not landlord costs. This is highly apparent in New Zealand, where mortgages are not fixed rates for more than 5 years; interest rate changes have little to no impact on rents, but supply and tenant incomes do.