But inequality arguably leads to unfairness though - is it "fair" that someone who is successful can get better chances for their kids through better environment, schooling and connections?
I'd argue that inequality pretty much always leads to unfairness.
Edit: And I say that as someone who pays for their kids to be privately educated at a prestigious private school because it is obvious that doing so gives them an unfair advantage.
And extreme economic inequality leads to people using their money to control politics and the media to stack the system in their favour. It's not simply the inequality that is the problem its what the rich choose to do with their money that is causing problems.