Here's a TED talk from a guy advocating Universal Basic Income. In it, he argues that people will not stop working because most of us have natural human ambitions for accomplishments.
I agree we all want to do something. But I think the modern entertainment-based world allows us to categorize non-productive accomplishments as achievements. Think of the feeling of achievement you get when you finish a show on Netflix, or (for those of us old enough) the feeling you got when you freed Princess Toadstool from Bowser.
How many people derive self-worth from food production? Some, sure, but as many as it takes to produce the food necessary to sustain all human life? I think a world that doesn't require work for sustenance will be a world with an overabundance of mediocre art, literature, and music, and a shortage of food, clothing, and shelter.