In an inflationary scenario both price & interest rate go up. The rent on a property mortgaged 20 years ago will be the same as a recently acquired property w/ similar features. Landlords don't charge less just because they can.
You should go look at all the empty storefronts in SoHo and on Bleecker Street and then come back and tell me that acquisition costs don't relate to the rents people charge. Storefronts and new developments there will often sit empty because if they charged what most people are willing to pay they wouldn't be able to meet their ROI targets and would go under.