The famous graphic about Napoleon's army which is very associated with Tufte is an example of a graphic that crams a lot of data into an illustration that rewards careful study. It's actually not a graphic that especially makes data about something obvious at a quick glance.
Sometimes an illustration that best serves as a background for a knowledgeable person spending 30 minutes explaining it is a good approach. Other times you want to capture the contrast between a few numbers in a compelling way.