The highest-density places, i.e. the ones with the most construction, tend to also have the highest rents, so empirically, the opposite of your claim is true.

I think the reason for this is that high rents stimulate construction. If you do a bivariate time series analysis with annual average rents and construction levels, I don't think you will find that increased construction raises rents.

I invest in real estate investment trusts (REITs). Analyst reports on apartment REITs project future rents inversely based on construction. Analysts believe that more apartment construction tends to lower rents.

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.

I don't think this assumption is always true.

For example, Estonia has been building many new dwellings, but prices are increasing incredibly, while a quarter of buildings stay unoccupied[1].

[1]: https://news.err.ee/1608648397/statistics-almost-a-quarter-o...