I think you are missing another potential implication: as less wealth is generated by productive citizens, and more from automation, there is less incentive for the ruler to maintain or improve quality of life.
For instance, they won't allow automation of this kind on their ground. As Ned Ludd would have it, they will keep the machines out and the humans in.
Suddenly their production is much costlier that what the robot-running neighbors produce. They can't export it (nobody would buy), but they can still locally consume it. But for that they need to limit the imports of the same thing to keep the prices up.
As the list of robot-produced goods grows, more and more import restrictions are added, and things cheaply available abroad become dear and inaccessible in the country.
I don't think a democratic government with a policy like that will last too long.
It looks more interesting to think how to distribute the ownership, a share in a huge robotic factory so that it is not easily falls under control of a single person or a small group. It might be an interesting game-theoretic problem.
Competition of democratic labor against automation is an interesting way to look at the current US popular support for tariffs and trade barriers.
Popular wisdom seems to look at China / Mexico manufacturing as supported by low labor costs, but in reality they're more and more supported by capital-intensive automation (enabled by the systems engineering expertise at running the low-labor cost plants originally).
The problem is that under communism, it's usually not ownership. You can't take away or sell your "share". All "communist" states I know about degraded to bureaucracy-run states.
Truly communist institutions, e.g. some monasteries, just abolish the notion of propery. They need unusually and highly motivated people to operate, though, that are few and fail to be mass-produced.
Once they're dying under an automated society which should be able to give them everything they need, social ownership over the means of production (some form of socialism, most likely) might seem a lot more palatable.
Welcome to the industrial revolution 2.0 where we once again have to wrestle with the question of who owns the means of production. Its an interesting problem and one that has been study a lot but not solved.