So yes, in our society, the desire to have more things than others probably isn't pathological, yet. But in the context of the kind of society I've been talking about talking about in this thread it would probably be regarded as a symptom of mental illness rather than a measure of social status.
[WS:] I would say that it is only true of societies in which accumulation of any sort is not possible, like in hunting and gathering societies. I think it is highly probable that these societies had status hierarchies as most mammal species do, but it was based on something else than accumulation of material goods. Perhaps on the conspicuous consumption of perishables - as the case of potlatch among Northwesters American Indians demonstrates.
Of course, there are countless other things outside accumulation or consumption of goods that can be the basis for social status, anything from physical or sexual prowess (often observed in low class males) to a certain look, shape of the body or the face, to skin color and to certain lineage. Given these choices, however, I would go with accumulation or consumption of goods, because these are the only ones that individuals can do something about. They are born with the other ones.
So paradoxically, wealth accumulation seems to be the most egalitarian way to social status achievement and display.
Wojtek