https://nlihc.org/resource/new-construction-has-mixed-short-... found new construction to have a negligible effect on the rents of high-tier buildings, and to increase the rents of low-tier buildings.

This is not too surprising, but may be specific to large and/or lax-on-immigration countries such as the US. It may look like an inversion of supply-and-demand, but the problem is the demand is essentially infinite compared to the change in supply that new construction brings. Without limiting new arrivals, all you've done is increased the desirability.

Like trying to reduce the relative amount of theft by increasing your inventory.