Interesting. It appears to me that I can better tell area differences between nicely shaped objects rather than long narrow objects. Is there a measure that can tell how nicely shaped an object is? The obvious one I could come up with is ratio of area of object to area of bounding circle. Closer to 1 is good. Lower than some threshold we pick is bad. I'm sure someone must have thought of this problem.
It certainly works to optimize squatter triangles over long narrow triangles, and these shapes over arcs.
This visual seems to better preserve the size of smaller markets, like Singapore and Australia. In a pie chart, they'd be indecipherable.