All the sciences mentioned above definitely do rely on controlled experimentation. But their central empirical questions are not amenable to being directly studied by controlled experimentation. We don't have multiple earths or natural histories upon which we can draw inference about the origins of species.

There is a world of difference between saying "I have observed speciation under these laboratory conditions" and "speciation explains observed biodiversity". These are distinct types of inferences. This of course does not mean that people who perform inference on natural history don't use controlled experiments: indeed they should draw on as much knowledge as possible about the mechanisms of the world in order to construct plausible theories of the past: but they can't run the world multiple times under different conditions to test their theories of the past in the way that we can test speciation.