As I argued in The Truthful Art, I believe that this is a self-defeating strategy because (a) sometimes an unusual graphic form is a good way to convey a message, and (b) by using it and explaining how to read it, you'll expand your audience's visual grammar and vocabulary —their “graphicacy”. The caption of this 1849 line graph is an example, and so are the thorough annotations that pioneers such as William Playfair wrote to further clarify their graphics.
The latest example I've seen of this strategy is this story by Zeit online. It isn't just a nice combination of strip plots, scatter plots, and maps; the authors inserted an explainer of how to interpret a bivariate choropleth map in the story itself. This one (the color choice has been critiqued, by the way):
“The diagram shows the distribution of medical practices in relation to private patients by county. Each point represents a district. The further to the right the point lies, the more private patients there are. The higher the point, the more medical practices there are. The red line makes the connection clear: many doctors are where there are many private patients.”Well done.
UPDATE: Jim Vallandingham has just published a good gallery of multivariate maps.