The leap from "controlled experiments are not possible" to "one has to deduce from first principles" is huge and unsupported. The results of controlled experiments do not exhaust the available empirical evidence by a long shot. We have a lot of data about the effects of monetary policy from around the world. True, inferring causality from this data is not nearly as straightforward as inferring causality from a randomized controlled trial, but it's still a lot more reliable than deduction from first principles, I would think.

Think about how your argument sounds when applied to cosmological theories about the very early universe. We have a number of different theories that cannot be simultaneously right, and we cannot conduct controlled experiments. Would you endorse deduction from first principles in this instance as well?