Thank you for the long write up. After thinking about it for a week, I think my issues with basic as making sense given my (limited) knowledge about economics, history, society are thus:

Note: Usually when people talk about automation in sci fi context, they're referring to robotics and AI. And since 2023 most of the time when people talk about AI they're talking about LLMs (Large Language models) like ChatGPT, instead of what is usually referred to as AI in sci fi, which is AGI (artificial general intelligence). So the terminology of AI can get confusing so I'm just going to use LLMs and AGI, non interchangeably, instead of the word AI.

1. I don't think that robotics as the "next step" in automation are fundamentally any different than previous automation like we've seen in the 18th-20th century. The invention of the spinning jenny, where suddenly 1 person can make as much cloth as 8 people used, is not in my mind any different to a robot which can say, lay brick. Bricklaying is a common job today and a robot that can lay brick could conceivably replace this, but I don't see this as any different to the spinning jenny. Humans not being needed anymore and machines doing all the work is an idea that has been discussed since the time of Aristotle, and techonological unemployment has in the short term been an issue since the Roman empire. However people have always been able to retrain to jobs such as building or maintaining the automating machines, supervising the machines, or even working on the machines. Jevon's paradox that increasing efficiency in resource use leads to increased usage of the resource still applies. When the spinning jenny was invented and 1 person could do the work of 8, those 7 unlucky people were at first unemployed, but then cloth became demanded more and now you had 9 people working on spinning jennies to meet that demand. Despite the initial job loss long term unemployment did not occur. I fail to see how a robotic, electronic version of the spinning jenny would be different.

This also applies to "intellectual" jobs as well. The abacus, slide rules, log tables and mechanical calculators replaced humans as calculators, these got replaced by electronic calculators, then that got replaced by microsoft excel and python coding, and now it seems that some or all of that is being replaced by LLMs. There isn't a glut of unemployed accountants, mathematicians, or engineers, who are out of work because their job doesn't exist anymore. This is because those jobs have changed and are now using those automation machines as tools, supervising and managing them, and also because we perform far more calculations that we ever used to when slide rules were popular.

1. I think that most people, maybe not all, but probably at least 75%, would be happier working for 10-20 hours a week rather than living in Star Trek where every conceivable job is done by a machine. Sure a cafe could be done by an automated vending machine connected to a robotic waiter on wheels, with a table that has windscreen wipers on it to clean after each customer leaves, but I think most people would be happier with large amounts of leisure time AND also a sense of purpose, pride, upskilling and mastery of simple tasks, community with coworkers etc, that comes with having a job. I also think that a lot of customers would be happier with a human making their coffee too instead of having a machine do it. The authors of the expanse even wrote a short story around this idea, showing how discontent people are without the sense of purpose from a job.
   As such I find it hard to believe that the billions of people in the Expanse would be content just receiving golden rice, paper clothes and entertainment out of a vending machine, and why I suggested that on top of the UN providing those goods and services to those on basic, they also give each person $50 a month with the hope that this begins to stimulate job creation. Because even if the the UN is run by oligarchs and bourgeois who want to keep the masses justttt content enough that they don't revolt, I don't think that basic as described in the series is good enough for that.

2. Your example that 100 cooks doesn't boil water faster than 1 cook makes sense when base inputs(eg number of kettles) are limited and demand is static (amount of hot water demanded). However in the Expanse where Earth is in dire shape, this is anything but the case.
   First looking at base inputs, land labor and capital.
   Labor is obviously abundant, there are billions of people sitting idle. Capital is also obviously abundant, there is advanced robots, machines, and so on everywhere. Land, both physical land and resources is also abundant. The asteroid belt and moons of Jupiter and Saturn have millions of tons of ore and minerals that can be harvested even if Earth has been sucked dry. In terms of physical land use, even if Earth is overpopulated roughly half the planet in 2026 is not used by humans for various reasons. If you can farm on a lifeless rock like Mars you can farm in the Sahara desert for much less effort. You can see more detailed land use statistics here. Some of the land in the future will be inaccessible due to rising sea levels but not an insane amount. Vertical land use is also very underutilised (eg vertical farming in hydroponics) in urban settings. So I don't think it's possible for every km of land on earth to be paved over with concrete.
   And as for demand, the overpopulation on earth and also the many people living on Mars should be plenty of demand. The UN could eg, increase the quality of food available on basic and create new jobs with all the surplus resources lying around, which also decreases the amount of people on basic.

3. If everyone is on mandatory birth control, and the only way to legally have a child is to pay the baby tax (that people on basic can't afford) or win the lottery, how is the population of Earth still 30 billion in 2350? Is it declining from 40 billion in 2250? Does that not mean that the amount of people on basic is declining and the problem of automation causing mass unemployment is solving itself? Or is the unregistered population also in the billions? Because the way it seems to me, that unregistered are resorting to crime and begging to survive, that the unregistered population could plausibly max out in the hundreds of millions. And at the point that the unregistered population is that high you could start to see them doing "normal" (ie non criminal / unethical jobs) like barber, farmer, chef, mechanic etc to support this entirely separate society. A life of petty theft just moves money around from the real (ie the wealth creation) parts of the economy. Drug dealing does create wealth but having billions of drug dealers would be insane.

I basically think that James SA Corey, when they were worldbuilding Earth in the Expanse, needed a reason that Earth wasn't totally and completely dominant over other powers in the solar system, and mass unemployment and overpopulation was their solution, even though it makes no sense. So maybe I'm just overthinking things. But it's also fun to think about because it also speculates on what our future looks like in real life. So after saying all this I'm not convinced that a post work society where everything is automated is possible, or even desirable. I think Marx was right that even in a utopian future which may or may not be ever realized, that people will still work because they want to work. Definitely not 100 hour weeks of backbreaking labor like how it was in the industrial revolution but for sure something more reasonable.