"Automation of the service sector" is meaningless. There is an infinite number of services that can be provided, and they can't all be automated. If you could really replace every single service sector job with robots, you'd have sentient androids, and in that case, they would probably value their own labor and become market participants.
If we're talking about 100% automation I agree, however what we're more likely to see is a situation more like what has happened with agriculture and manufacturing. What was once a source of many jobs asymptotically approaches zero over time. Within our lifetimes you're going to see a situation where less than 10% of the population can add more value than it costs to employ them. That will still mean nearly a billion people working, but what exactly are the other nine billion going to do? In the past the answer was to move to another sector of the economy, this time that seems unlikely.