There's one huge flaw in the whole thing.
It assumes demand for goods in general is really elastic.
The people of old who predicted automation would bring about a three-day work week were wrong because they assumed demand would be inelastic: That the people would want only so much 'stuff' and so with increasing per-person productivity there would come a point where that demand would be satisfied with only a small number of people in employment. This didn't happen, because with falling cost of production consumption increased accordingly: Even the low-income today live a lifestyle that would have been the envy of a preindustrial king. Clothing so cheap that people will throw away a piece rather than spend time stitching a hole? Items imported from half-way around the world just to decorate our homes? Holidays to exotic locations?
If we all lived like an 1800's peasant, we really would need only a fraction of the population in work.
An important question is how far this can be taken. If further automation leads to even greater per-person efficiency gains, what happens? Do we reach the point where clothes are so cheap people will throw them away each day rather than wash them and just buy anew? There has to be a limit to how much useless tat people want in their lives - and there are only so many hours in the day to watch television. Even if consumption continues to increase, there are other costs to this solution: Massive resource usage and environmental impact.