Income inequality is an indirect, at best, and irrelevant at worst, measurement.
One cares about the average health, wealth, and longevity of a population.
A thousand people pack into a conference hall: Bill Gates plus 999 homeless people. "Average wealth" says that the average person there is a multi-millionaire. Is that an appropriate measurement to use?
A week later msoft's stock has a major uptick, and "average wealth" says the average person there gained 15% . Still a right measurement?