"I think that's the nub of the issue here. I believe that influence diagrams IDs mathematize and formalize Wright's path diagrams but I find it hard to believe these fancy graphs are explanations rather than a description/model of causation. They are 'just' CS data structures??"
In statistics, DAGs are just a systematic organisation of knowledge or believes about phenomena. They don't explain anything, because statistics isn't supposed to explain - it only helps to validate the researcher's theory/prior*. Still, such description was lacking in many places before Pearl, e.g. "explaining away", which his formalism explains in an intuitive way.
*I'm a hard-core Baysian. Not that I think that frequentists are wrong. They are right in some (trivial and useless) cases.