Why are causal inference diagrams so useful or effective? Is there a short explanation of why Pearl's casual inference diagrams are so highly-regarded, useful or effective?
I can't help but think it's just so simple an idea that I can't tell why it could be such a big deal: It's just like a set of equations where functions are composed in an 'acyclic' way? And apparently it's like groundbreaking and there's a whole field of 'causality'?
 A: There are two prongs to this answer. First, why is the New Causal Revolution useful? For reference, see my answer on CrossValidated. The New Causal Revolution is useful because it allows the researcher to gain causal information, given the right model and data, from observational studies with no manipulated variables. Before the New Causal Revolution, the mantra was that you had to do an experiment and manipulate variables to get causal information. There are still Design of Experiments books that baldly (and incorrectly) state that you have to do an experiment to get causal information.
That you can get causal information, now, from an observational study is especially important for fields like medicine, where often the experiment you might like to run is unethical.
Second, Pearl's causal diagrams allow the researcher to gain some information even without any Structural Causal Models (SCMs) (the "set of equations" to which you referred). By putting together the causal graph (which can either be learned to some extent through data, or assembled by subject matter experts), it is possible to determine the answer to questions such as "If we are interested in the causal effect of $X$ on $Y,$ which variables do we need to condition on to get an unbiased result?" There are various graph algorithms that can be run on the causal graph, again without needing to refer to SCMs.
I am actually working on a project right now that uses causal diagrams in a very simple way (not doing any graph surgery or counterfactuals) just for reporting. And that reporting is of very high value, because it allows us to track processes all the way from start to finish.
