The reason people care about inequality is that under capitalism, it's the measure that best tracks with quality of life in the lowest standards of living. Why

The reason people care about inequality is that under capitalism, it's the measure that best tracks with quality of life in the lowest standards of living. Why is capitalism relevant? Because the driving economic force under capitalism is that the rich (capital owners) want to get richer (earn returns on their capital investments). Why doesn't a rising tide lift all boats, in practice? Because that doesn't maximize return on capital. The people who financed development and operation of a hospital get the best returns on their investments by pricing things out of reach of those with the least. You don't maximize area of a rectangle under an income distribution curve by making the lowest point of the curve the top of the rectangle. Perhaps the best way to think of it is "a rising tide lifts all boats, but some of them aren't lifted by as much as the water level has risen." Not quite as snappy, is it? It does get the point across, though. Inequality functions as a measure of how many boats aren't keeping up with the rising water level. That's why so many people care about it. It's the same thing as your goal, but bundled up as an aggregate and easy to track, instead of involving hundreds of subjective measures. No measure is perfect, of course, but it's a lot harder to game than something like the CPI is.