That is not how rent prices work. It is pretty much supply and demand. No one cares how much your financing costs. If people start losing their jobs because the FED induces a recession, that means less money for rent. Younger folks move back in with their parents. People take on an extra roommate or two. Demand for rental units goes down. Prices go down.

If a significant fraction of landlords have financing costs that greatly exceed rental income, that is their problem. They can't just pass that cost on to renters because they feel like it.