It's a bit surprising that this graph appears so infrequently; it would appear to be especially useful for political scientists showing voting fractions over time (with the three most prominent parties for each axis), economists examining the composition of an economy (such as above), or sociologists examining over-time trends in any three-part categorical variable (such as "agree," "disagree," or "neutral" on a question of values or attitudes).
However, note that simply because a graph looks like it's a ternary plot does not make it one! For example, Junk Charts dissects this pseudo-ternary plot in the New York Times.
