Paul, my use of standard deviation is a clear givaway to my original education as an engineer :-)

My thought process on that particular measure is two-fold:

1) Like the quintile metric you mentioned, it will help measure the gap between the highest and lowest income households, because the more data points at the ends of the spectrum (and the further apart they are) the greater the standard deviation.

2) It also gives some measure of the degree of polarization, because a large population near the middle will help reduce the standard deviation, leading to my comment about the middle class. The highest/lowest quintile gap doesn't tell you anything about what's going on in the middle three quintiles.