> Every time someone in history has tried to remove the gap it's ended in horror.
Has it? It's easy to recall the times it has because they make it to the history books, but there's been peaceful periods of reduction in income inequality too. Simply in the US, in the period right after WW2 income inequality fell in what is known as "The Great Compression"[1].
This was also an era of incredible progress and development of the US— everything from big developments around social issues (civil rights movement), huge cultural evolution (counterculture), big development in science and technology (moon landings, nuclear power, etc).
When people don't have to worry about wether they can afford rent the next month, they can worry less about losing their job to immigrants, they can afford to quit a bad job to find a better one, open their own business, etc. In general not things you measure as economic standard of living, as the money you make and things you own, but that translate as less time spent stressed and more time spent being productive both economically and just culturally.
The thought that to make things better for the poor we need to make them better for the rich too is awful close to trickle-down economics, which have proven again and again to be very much an unsound theory.
[1]: https://en.wikipedia.org/wiki/Income_inequality_in_the_Unite...