First, inequality is unstable for societies. Small hunter-gatherer societies always had to be basically egalitarian because they could not survive the societal stresses and internal resentments that came from people having too much more than other people, even social status. One way anthropologists have written that tribal groups would achieve this was by downplaying the roles of their biggest contributors. The other men would do things like stating that the massive boar the best hunter had killed was just a runt and not anything to be proud of. This keeps egos in check and makes the less successful less resentful. Everyone would still be aware of the hierarchy and who contributed what but there was no flaunting that would start fights.
When this resentment gets too severe and is combined with real or perceived scarcity of resources, even large-scale societies get pretty crazy, especially if people start reading stuff about fairness and the rights of workers and such. The Chinese Great Leap Forward, the French Revolution, the Soviet Bolshevik Revolution. Lots of rich people got killed as well as plenty of others who just got caught in the cross-fire of revolutionary madness. If people are feeling the pinch too heavily while seeing others bask in the lap of luxury, they tend to get a little murderous.
The truly epically rich, the 0.000001% are generally so disconnected from the masses that they are like a different species. Everything about their lives will be different from that of a normie. In the same way we tend to see animals as less than humans since we can't communicate, the uber-rich will see the poor as less than themselves since they don't communicate with them.
Some Aboriginal groups up north are forced to cull stray dogs in their communities every so often to keep them from getting out of control and dangerously feral. However, people also treat their own pets like a part of the family and would never hurt them because you know and love them and don't want to see them suffer. This is what needs to happen with the poor. The rich need to know of them in more than the abstract or else they won't really mind having them suffer. Close-gated communities create a dangerous Us vs Them mentality by inadvertently dehumanizing those on the outside.
Second, inequality is unhealthy for societies. In their work, The Spirit Level: Why Equal Societies Almost Always do Better, Richard Wilkinson and Kate Pickett show that in societies where wealth is more equally distributed, the population is better off in almost every way. They compare countries with each other but what I found more useful was their comparison of US states since there would be less cultural and geographical differences that could explain these outcomes than there would be between countries.
Essentially, inequality was linked to worse physical health, mental health, drug abuse, education levels, imprisonment rates, obesity, social mobility, community trust, physical violence, teenage pregnancies, and child well-being. Only suicide was more common in more equal societies, likely because it's harder to blame others when things go wrong when a society is kept more equal.
It might be worth noting that Denmark, the most equal of the 17 developed countries discussed earlier, is also the happiest country in the world according to the the people's response to a survey. Next was Norway, the second-most equal. It mixes up a little bit after that but the general trend remains that more equal countries have happier people. Canada's actually sixth most happy so we're happier than our inequality should dictate while our southern neighbor is seventeenth, which is exactly how happy they should apparently be.
Interestingly, New York was one of the outlier states in The Spirit Level in that it has high inequality but suffers less from the problems of inequality compared to other US states. Perhaps this is because the rich and poor intermingle much more in New York City than elsewhere in the country?