I think there's an implicit assumption that housing stock is sufficient to house the population, and that landlords compete with each other. So rents generally trend downward, and track the costs of owning and maintaining a residence.

When those costs balloon (because of a glut of buyers with cash to launder), so does the prevailing rent which legitimate purchasers of real estate need to charge to recoup costs and make a profit.

If on the other hand housing stock is insufficient, rent will simply track demand and this effect will be masked.