1. First let's get through the easy part: reinforcement learning (RL) is not unique in its ability to identify cause-and-effect - this was achieved long ago through the use of randomized controlled trials. RL merely streamlines the task of reacting to such information (as well as optimizing experiments w.r.t. a desired goal).
2. Now the trickier part: you can learn causality from observational data alone if you combine this with understanding of a mechanism. Indeed, the whole field of causal inference is an attempt to formalize and extend such methods.
There is a massive space of problems where experimentation (whether old-fashioned A/B testing or more sophisticated online learning) is simply not possible, whether because of ethical reasons, cost, or other reasons behind non-destructive study. These problems are common in medicine, economics, physics. In such problems the only data is observational. Causal inference is very valuable here.
Let me try again: the most interesting and frequent setting is where you cannot control the experimental conditions and you have no idea about the causal mechanism at play. And that is where traditional ML cannot help, but RL can.
It should not be underestimated that our collective knowledge of causal inference with statistical methods is good, but still improving.
I mean, in that sense, ML is helpful. Heck, it is already used in causal inference in two-step estimators and the like.
Or better yet (stretching and sidestepping how you meant it), give your friendly neighborhood statistician/econometrician just a dataset and they can't do causal inference. Give them propensities and column names/descriptions and a writeup of the experiment/where the data came from, and suddenly they might be able to do causal inference. It points to a need to augment our observations with more structured metadata, if we want to do causal inference with data that's just lying around.
It seems that any theorem that rules out learning causality from observational data alone would also rule out learning causality from any kind of interactions.
Unless you're assuming that agent A "knows" it has free will so its own actions have no cause, while agent B can't tell whether the environment caused agent A's actions or vice-versa. But if that's what the proof hinges on, it's pretty shallow, because agent A has no such guarantee that its own choices have no root cause.
What I meant is that you cannot learn from "general" observational data, unless it is structured in a certain way (the randomized controlled trial mentioned in a sibling). RL is able to gather data on its own, while other ML methods must do with what they are given. This means that RL could eventually discover the causal relationships, while non-RL cannot (except if the data comes from a RCT).
Because in statistics, causal inference is certainly possible without RCTs.
As others have pointed out, this is kind of the point of much of Pearl's work on causality. Specifically, do-calculus provides a set of primitive operations that can be used to convert queries in interventional/counterfactual (causal) distributions to estimands in a purely observational distribution.
Though I agree that this is an important next challenge (and causality has been the "next challenge" for at least the last 5 years), it's often more easily solved these days with mixing in human expert knowledge to the equation (that is, using ML alongside of human expertise).
Reinforcement learning is uniquely positioned to build machines that understand cause-and-effect on their own because the algorithm is allowed to interact with the world, observe the results, gather more data, rule out hypotheses, and so on.