Childless couples aren't competing for 4 bedroom apartments. The problem is that cities forbid construction of those.

Neither do families, as that's out of reach financially. In a dense city centre a three bedroom apartment is already a sign of wealth.

Everyone is competing for space. I don't see how cities prevent building larger apartments. European cities are mostly built out anyway, and the tendency is rather more to split large apartments to cater to the childless crowd.

Cities prevent larger apartments through onerous zoning codes. It's so expensive to build because of the permits and the risk that only a narrow type of structure has a chance of profit.

> mostly built out

Look at rent in Asia. They actually build towers over there and they build large apartments for families as well as small apartments for couples. There's enough building that the housing market is diverse.

Architectural preservation. Which may not be all a negative thing, but central Paris is low-rise compared to Manhattan, Berlin or even central London.

Central Paris is denser than Manhattan. At some point the bottleneck is not the amount of people you can cram into a m2 of land, but the underlying infrastructures.