“A federally funded and locally administrated job guarantee available at the discretion of the worker and paying a liveable wage with benefits would replace the minimum wage, so we wouldn’t have that bit of idiocy suppressing our economy.”
How is this unemployment benefit at a liveable wage less idiocy than the minimum wage? Who would seek real work if they had a guaranteed liveable wage for doing next to nothing? What you are proposing is the Universal Basic Income, except that you have to work for it at some meaningless make-work dreamed up by a bureaucrat. Probably picking up litter or cleaning graffiti off walls or some such thing. Government work schemes have never been a good substitute for a real job.
“In fact, capitalism will seek efficiency (fewer employees) by definition.” Not quite true: a company will continue to hire more employees until the next employee’s wage exceeds the extra income the company can make by hiring an extra employee. It is true that Companies seek higher productivity from each employee, but a successful company can achieve higher labour productivity and still hire more staff at the same time, as long as there is demand for more product than they can currently make.