As Chris Wales acknowledges, the "equality" question is so broad and deep that it deserves several posts rather than a few comments. After all, R H Tawney wrote a whole book about it.
So here are a few rejoinders to the detailed and thoughtful comment Chris has made to the previous post
1. Is promoting equality designed to save the rich for themselves of to save society form the rich?
Both really. As Wilkinson and Pickett show, the rich themselves are happier in more equal societies. I think this probably arises from "all being in it together" (and having to spend less time and effort protecting their wealth from the dispossessed.) Perhaps David Cameron's attempt to measure happiness will confirm this.
But equally democratic societies meed to be protected from the rich who, through being disconnected from society, and, believing (mistakenly) they have no need of it, withdraw their support from the means of sustaining it. In addition the very rich can and do wield undue influence in trying to manipulate the political process to preserve their privileges, not only for themselves, but also for their offspring. Why else is no party prepared to introduced effective inheritance taxes?
2. Some rich are philanthropic.
Yes of course they are and thank goodness for them, especially Bill Gates's foundation to combat AIDS in Africa. But neither national nor international society should be dependent on the whims of the rich for "good works." The rich should pay realistic taxes to repay, preserve and improve the societies which have enabled them to prosper.
3. People who strive should be rewarded.
They should and they will be, but that does not mean they should become so disproportionately rich in material and financial matters that they endanger democratic health. Even in societies with a high measure of equality (which, to repeat, does not equate to "sameness") individuals will still strive for job satisfaction, the good opinion of their neighbours, political power, sporting prowess, domestic happiness, and, for those for whom it is a priority, a superior level of material wealth.