For example, understanding why certain estimators give you the average treatment effect on treated individuals rather than the average treatment effect on everyone is easier if you understand the mathematics of it. But you need to know basic probability and mathematical statistics.
Causal mediation analysis is similar if you want to understand what assumptions you really need to make to talk about the mechanisms through which a treatment effect acts on the outcome.
I rest my case. If someone told me that the only way I was going to notice something is with the stuff you are saying, I'd be pretty reluctant to trust them.
If you're talking about optimizing around some agreed upon thing, sure I can understand the idea of using some more complex statistical analysis (though I might question the incremental value).
I am not saying that a convincing answer has to be convoluted. But a simple answer is not always the right one.
To understand when a simple answer is unlikely to be correct, you do benefit from understanding the mathematics. There’s a reason that people with doctorates in statistics spend 8 to 10 years in school to learn how to contribute to it.
Causal mediation analysis is similar if you want to understand what assumptions you really need to make to talk about the mechanisms through which a treatment effect acts on the outcome.