> supply increases until demand is met fully

That is a very optimistic view.

What I've seen in Finland and UK is pretty much the opposite of what you claim. In both countries the housing supply in growth centers is essentially controlled by a handful of huge developers. In an attempt to make the planning permission system more comprehensive, it has only turned out more complex and expensive to navigate. That means that only the largest operators can afford to work within it.

In both countries we see developers deliberately restricting the speed with which new housing stock enters the market. In UK, the common pattern seems to be to sell a floor or two at a time, while the others are still supposedly under construction. In Finland, the developers literally shut down their sales and rather took a hit in maintenance costs than sell their available stock while the market was too slow.

Your assumption therefore makes a crucial mistake - it stems from an assumption of perfect markets and unrestricted housing supply. In reality neither of those two hold true.

Rent rises with the productivity of locations, and density makes locations more productive in the aggregate. Agglomeration is the economic term for why that is.

It may seem paradoxical to you, but supply and demand simply doesn't function the same way when it comes to land. The supply of land is fixed. That is why rents are more like monopoly pricing.