In one of the chapters of Visual Revelations, Wainer explains trilinear plots, and asks himself why they are not common in the media. I'm planning to quote these lines in future writings (highlights below are mine) as they are relevant for any discussion about when it is appropriate to avoid conventional graphics in favor of more unusual or innovative ones:
Despite their frequent suitability, trilinear plots are rarely seen in the media. Why? Certainly part of the reason must be convention. There is a cost involved in bucking convention and using an innovative graphical form. Thus, whenever an innovative graphical format is proposed, an important consideration must be the gains associated with the new form versus the losses associated with moving away from the conventional display (...).
It was my intention (...) to provide the reader with some experience, and hence comfort, with the format. By my doing so, perhaps others will produce evocative applications of this somewhat specialized format. Thus can we expand the public consciousness of our graphical repertoire and continue to increase the comprehensibility of information.
Trilinear charts are certainly rare in news publications. The only recent example that came to my mind is this one, by The New York Times: