"The traditional approach has tended to obscure the nature of the choice that has to be made. The question is commonly thought of as one in which A inflicts harm on B and what has to be decided is: how should we restrain A? But this is wrong. We are dealing with a problem of a reciprocal nature. To avoid the harm to B would inflict harm on A. The real question that has to be decided is: should A be allowed to harm B or should B be allowed to harm A?"It's true. This is an important question. But in practice most people talk about Pigou because they have thought about that question and answered it or because the parties have resolved it themselves but we think that the resolution came about under duress.
And I promise you, that doesn't mean you need to explain Coase to us.
I told my students on the first day that economics is progressive and although sometimes adversarial (say, Friedman vs. Coase in a seminar room) it is not factional (there is no great Pigou vs. Coase war - ignore people who act like there is).