Whatever else you might say about inequality, "unsustainable" is an obvious falsehood.
Roman civilization, for example, lasted two thousand years. Eight times as long as the United States. Think about that. One hundred generations of men lived and died as Romans. And the Roman Empire featured radical inequality, of the sort that we could never have in modern America, no matter what the Gini coefficient was.
On one side was the Emperor and his soldiers, who could have you and your entire family tortured to death, purely on a whim (see Caligula). On the other side were slaves, who had no human rights at all and were treated as property. And between them, countless peasants starved to death every time there was a bad harvest, while countless aristocrats taxed their lands to fund lavish banquets. (In the Roman tax system, tax collection was outsourced; the tax collector was responsible for finding a certain amount, and anything above that he could keep for himself.)
That's some serious fucking inequality right there. And I'm certainly not saying it's a good idea, or that we should try to emulate them. But it was, as a raw historical fact, extremely sustainable, lasting eight times as long as the US has so far.