Get hold of a copy of Tony Judt's Ill fares the land. It has references to the correlation between inequality and many measures of 'problems' and tries to make the case for a causal link. Also explains philosophical background.

>get income inequality in check by whatever means and most of your problems go away.

Is that a cause or an effect though? As in, if your society evolved in such that "most problems" don't exist or aren't serious, then maybe as a consequence there isn't a lot of income disparity. But that doesn't necessarily hold in reverse. Making incomes equal by some method doesn't necessarily make the problems go away.

https://philoofalexandria.wordpress.com/2010/09/25/reynolds-...

Certainly large amounts of some kind of equality is needed for a democracy to work.

Barely!

The point in discussion, everyone likes equality in a way they having it, without they having to do anything about it. Or in other words making the rich poor in some way. Wasn't this what communism was all about.

The real issue is equality in access to basic resources, which is by and large there already. Beyond this you need to let people win and lose on merit.

You don't go around paying the same money for a haircut and brain surgery. That sort of equality doesn't work. Or to be more precise that's inequality of a very worst kind.