Most seem to miss the bigger picture with this study. People don't like rank in general, even when it's reversed. In other words most people, in there heart of hearts are communists and would prefer a classes society.
Egalitarianism is not Communism. Humans have had agriculture for about 5,000 years and states with hierarchy about the same amount of time. Before that behaviourally modern humans were around for ~200,000 years. They lived in bands and tribes that may occasionally have gotten as big as 200 people, almost all of whom would have been either related or in a relationship with a relative.
Humans are egalitarians and would prefer a classless society. Ants are Communists.
Humans have and have always had social status structures, reaching back into evolutionary time. This is why such a huge portion of our psychology is devoted to dealing with status issues.
Animals have status too. Various primates form stable status hierarchies in their bands. Chimps are a great example. Canine species do this as well. And other animals, too - all the way down to lobsters. Basically any animal with any intraspecies interaction has some concept of status hierarchy.
And like the animals, humans like their hierarchies - the hierarchy fulfills a psychological need, the way being in a herd makes a herd animal feel safe.
People like knowing where they stand. They like having a role to play and knowing others are playing their roles. Without a clear hierarchy people feel nervous, the way a dog acts out from anxiety when the humans don't take charge.
Some people are driven to climb the hierarchy but most just want a stable existence somewhere in the middle of the pack where they can "camouflage against the herd" and avoid being noticed too much.
Most people like security and dislike responsibility for hard choices. Having others of higher status to take on those challenges absolves them of the need to make such decisions.
Egalitarianism is definitely also a part of human nature, but it's as a psychological counterpoint to the status hierarchy. People want the hierarchy to exist - but they want it to seem fair and legitimate and they want people to deserve their positions. People only dislike a hierarchy that seems illegitimate according to their mental heuristic.
So no, humans would not prefer a classless society, and such a society can never exist. If it existed for a moment, it'd cease to exist the next since classes would instantly form along the various dividing lines between groups of different personalities, proclivities and capacities. Level everyone's wealth and you quickly just end up with the same distribution as before, as we've seen after various bloodbaths in China, Russia, etc.
Having social status structures doesn't mean having social class. I don't see anything in what you wrote that I'm not in agreement with. Violent agreement for all.
