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.

You think you can make a law that sets the price of housing above local wages and stays there?

No, you actually cannot do this in any lasting way.

The price of land would fall to the level required to make it construction viable again. Or the city would be abandoned, which is not generally the outcome since cities have so much shared capital investment that cannot be moved elsewhere.