The concept of a society with a strong form of equality is, I think, an utopia, and AFAIK, no such society exists. Even if you look at primitive societies, there are better hunters, the tribe leader has more wives than the regular guy, the shaman is revered, etc.

One can say that's not what this discussion is about, i.e. it's the potential for equality, the right to be equal rather than the radical definition above, but then the discussion becomes muddled, how to measure inequality, economically (e.g. the Gini index), by asking people, etc. "Inequality" then becomes a very complicated word like "democracy" or "justice".

I think it's interesting to draw a comparison with democracy: "true" democracy, i.e. radical democracy, is likewise impossible to maintain. The closest form in Athens degenerated to tyranny many times. And probably Athens was the largest collection of people where such pure democracy is feasible, i.e. it cannot be scaled up to a whole country. Judging from the lack of other examples in human history, one can see that the order of things in Athens was not the natural state of society.

So, I maintain that pure forms "liberté, égalité, fraternité" are not practical and cannot be achieved.

Now, one can argue back, saying "Yeah, yeah, we know that, but surely you can rank countries on how much they have achieved these, e.g. surely no one would debate that the US is more democratic than Saudi Arabia." This, of course, is true, but (i) means that we should leave behind "a brotherhood of men, and no possession, too" crap behind and (ii) leads us back to the question of measuring inequality.