So there's no in-between stage; it just pops into place? I don't know what you are getting at.
There's the difference between our positions - I don't believe we'll hit a post-scarcity world; I think that that every single system humans live in will be subject to the constraints of scarcity.
You, on the other hand, treat it as inevitable. That's why you offered your hypothetical of robots that are able to obsolete human beings - a belief that that endstate will show up.
We're not going to agree on that assumption, but you could offer an argument why that assumption is relevant and reasonable.
Note that Rome faced a similar problem as slaves did and could do most of the "grunt work". There were more citizens than jobs.
Alternatively, rather than Rome running out of jobs, Rome had become spiritually decadent and created a privileged "citizen" class who survived solely on the enslavement of others. It had a system that relied on the growth and maintenance of the slave class keeping up with the population of the "citizen" class. When such did not happen (too many citizens consuming entertainment instead of keeping the slaves in line and productive), the system crashed.