Nope.
Rents cannot (at meaningful scale) exceed local productivity, or else there will be widespread vacancies and landlords will reduce their rents.
Rents cannot (at meaningful scale) fall below local productivity, or else landlords will simply raise their rents.
Go talk to a landlord about how they site prices.
Step 1. Look up income of your target demographic
Step 2. Eat 30% of their income
Can you show me a place with high local productivity and low rent?
Can you show me a place with high rent and low local productivity (that's not e.g. a vacation destination for people with high productivity elsewhere)?
You can certainly artificially suppress prices with rent control. But that just gets fed back into the system in the form of reduced supply, so it ends up raising rents on the non-controlled housing stock anyway.
> Can you show me a place with high local productivity and low rent?
Put the following prompt into your favourite AI and enjoy the reading:
"How do rents relate to productivity in the area? How does Vienna compare to San Francisco?"
Assume you have an area with a certain productivity and rent. Population and housing are growing at a certain rate.
Now make a law that makes construction cheaper. Or make a law that makes construction more expensive. What happens to rent and mortgages, even though productivity hasn't changed at all?
Productivity (or, rather, wealth) of the occupants is a very strong factor, but it is still just one of multiple factors.