For the sake of argument, I'm reducing the value of social status to its effect on widening the "field of eligibles" - that is, increasing the quality and quantity of potential mates. When in mate-seeking mode, we look around to see who’s available and who we think we can attract. Social comparison is the game. Inequality of mating opportunities is built into this game. Even if everyone were more or less the same on wide range of characteristics, the participants in the game would find ways to make finer discriminations. So there will status hierarchies. (No, this isn’t a justification of extreme income or wealth inequality.)
I'm leading to questions about what should we want of society and government. If there’s a solid safety net (basic security for all: housing, nutrition, health care, and education), is that good enough? Or should government policy seek to promote a flatter status hierarchy, where status differences are smaller in society at large?
The guaranteed goods and services would be pretty much the same under either policy objective: housing, nutrition, healthcare, and education. The difference would be in determining how much is enough. Given the propensity of humans to sort themselves by status, I suspect that serious policies to minimize status differences would be defeated by more intense status competition within the collectivity and the emergence of different kinds of status markers.