I agree that even a post-scarcity society would need some form of employment to determine status and so on. But that seems irrelevant to the current problem: one where even people who are not interested in status need to work long hours in unpleasant conditions just to pay for food, housing, and medical costs, and where ease of access to these goods hasn't kept pace with technological advantages.

But that's not the case in the modern developed world. If you are really indifferent to status, you can easily get enough food, housing, and medical care to survive by sheer freeloading. This is true even in the U.S., let alone in more extensive welfare states.

Of course, completely forsaking status would mean all sorts of unpleasantness for a typical person, but this is only because we hate to admit how much our lives revolve around zero-sum status competitions after all.

I think a genuinely post-work society would have its own ways of producing status based on hobbyist communities, social interaction, and excellence at arts/scholarship/sports/hobbies; the old European nobility was able to handle its internal status disputes in this way, though I don't know how much fo that depended on them knowing in the back of their mind they were all superior to the peasantry anyway.

Don't forget about the status obtained from having power over others. That's one part of the human nature that's always dangerous to ignore. (The old European nobility was certainly not indifferent to it, and not just towards the peasants.)

Also, there would always be losers in these post-work status games who could improve their status by engaging in some sort of paid work and saving up to trade for the coveted status markers. These tendencies would have to be forcibly suppressed to prevent a market economy with paid labor from reemerging. It's roughly analogous to the present sexual customs and prostitution. Men are supposed to find sexual partners by excelling in various informal, non-monetary status-bearing personal attributes, but things being zero-sum, many losers in this game find it an attractive option to earn money and pay for sex instead, whether through out-and-out prostitution or various less explicit arrangements.