In the long term an economy should be in equilibrium. That is: in every part of it as much money should go in as goes out.
The present Western economies obviously aren't in equilibrium: inequality is increasing. As the rich spend less and differently that means falling demand for many products. To repair that we have quantative easing - the cowardly cop-out by politicians afraid to raise the taxes on the rich. The problem is that it is not a real solution: after some time all the extra money will leak away towards the rich and the next stimulus is needed.
The world has faced a similar situation in the 1930s. Roosevelt too faced the problem that he needed to keep stimulating the economy. As soon as he relaxed the depression came back. Things only changed structurally after the war had led to a huge increase in the taxes for the rich.
Of course it is possible to imagine a country that is stable at a larger inequality. Piketty describes it as the 19th centrury's Jane Austen society. And at the moment Latin America still has a very similar society. But such a society as a whole is by definition poorer. Inequality is primarily about driving the poor in a more dependent position. They will get worse education, spend more time unemployed and their economic position will be more unstable. There needs to be a permanent "labor reserve" in order to keep the wages down. As a consequence their contributions to the economy will decrease. The contributions of the rich - on the other hand - will not increase: they will just get a bigger part of the national wealth at the expense of the poor.
Rising nations typically put a lot of effort in providing education, healthcare and other services to the whole of the population. They know that that is the key to economic growth. Even retirement benefits fit in that goal as they liberate the workers to focus on their jobs. But in the rich countries that goal tends to slowly get lost. Those still supporting more equality start to use bland arguments like that it is a sign of civilization. But that is a very subjective argument that can mean different things to different people.
So the road towards a more unequal society is a road with a shrinking economy. And that also means a shrinking tax base. This at a time when the demands on the system will increase due to an increase in the number of poor. That will cause demands for government budget cuts, resulting in more poverty. So there is self reinforcing process going on here.