Quite the opposite I think. Our machines can 'already' work well enough to provide free food, shelter and education to every person on earth. Even still, we produce food for 10B people yet hunger is a problem.
If everyone was given free food, shelter and education, then everyone would fart around and get bored until some of them hackers gather to build a space-ship and others join in. Utopia? probably. But the real problem is broken distribution model which real means broken governance model.
Secondly, are you sure all work can be done by currently-existing machines and people willing to do that work for fun? For example, maintenance on a broken sewage system. I think there's going to be some jobs that machines can't yet do, no one wants to do, and yet still need to be done.