People with literally billions of dollars of wealth still devote time and energy to earning more. I don't think its a stretch to think that people who merely have enough for tolerable food, clothing, shelter will continue to do so.
If I look at the size of the median house, the price of the median car, that doesn't seem true. If most people would be satisfied with a basic income scheme and nothing more, why aren't most middle class people trying to save half their paycheck and retire before 50?
For a minimum wage worker it is absolutely trivial to see that the tradeoff isn't worth it and subsequently they behave predictably like a lazy person. People acting according to free market logic deserve the stick. Do you see the problem?
Let's say you got $20k/yr[0] for free. Do you think you could live comfortably on that? Would you be willing to work to improve your comfort level?
[0] full time US minimum wage with no time off is about $15k/yr
You work to be able to afford nicer clothes, more vidya games, fine whisky, more-comfortable retirement when you do stop working, vacations, better school for your kids, a nicer house with a view, and so on.
The carrot remains the same, the stick is just somewhat smaller.
Which raises the question of why anyone would work, if doing whatever you want and still living a comfortable life was an option.
It sounds like a lovely future, but I don't the automation exists yet to replace all the jobs.