People do stop working when it's all provided. Anyone with simple pattern recognition has seen that happen, not everyone of course, but a lot give up. Like this pattern I noticed of people saying stuff like this pretending to be altruistic and empathetic but really are just salty they don't have the money to lie around all day.
I won't deny that a portion of the population would definitely do this, but I don't think it's a majority. There's a nontrivial number of people who would stop working because they don't need to anymore, eg, working mom's with supportive spouses who work a menial job just to help cover the bills. They would definitely leave their work and spend time with kids and being a homemaker. Some would quit and do nothing because they're lazy. Sure.
I don't think that's the majority of the workforce. Many people, such as myself, do it mainly because they want to be productive and/or help people. Those like me, who are also happy with their employer (I presently am quite pleased with my boss/management), would not really do anything differently.
I think the root of what you're seeing is that if the basic needs were covered, people would quit bad jobs. Bluntly, there are a lot of bad jobs out there. I would venture a guess to say it's the majority. If someone hates their workplace but they need to make rent, they're more likely to stay with a bad job so they can have a place to live; these people, if their needs were met, would walk out in droves. That would be enough to move the needle over to a majority.
My argument from your statement can be rephrased as: if we met everyone's needs, they would have no reason to stay working at jobs they hate.
That's not what UBI tests have shown us in practice.
Anecdotally, a close friend of mine made enough to retire several years ago and now he just works a job he finds fulfilling instead of the highest paying one. IMHO humans instinctively want to contribute to the tribe.