No, let's assume we get there as well and everybody is free to choose whatever the hell they want to do with all their free time -- that kind of world. Assume that you wake up in that kind of a world and decide that today you will climb Mt. Everest, because well, you know, you can !
So you train virtually, buy all the needed supplies and get them delivered to your house with no human intervention automatically, book your flights, get on a plane that flies itself and land at the base camp. Now what ? well you have to find a sherpa and hire him ...why ? because you just can't do something for the first time all by yourself even if you have all the tech in the world. Work (although not as we normally define it) is simply another way to say 'having experience with a certain skill for a sufficiently long amount of time and doing it at a sufficiently reasonable level of proficiency that it is of value others that do not have the experience'.
The sherpa example is just for making a point but even if we limit the discussion of machines doing all 'work' -- who will build the machines that build the machines ? who will look after the machines that look after the machines ? who will teach those who build and look after the machines ? ...and why would any of these people to do any of these things that obviously don't come naturally but require time, patience and perhaps some skill to master ?