Basically, nothing can be free, as nothing is an infinite resource.
If we can avoid destroying ourselves to get robots reproducing, and benevolent, smarter AI than what we are, tech should have advanced to the point where: Energy = whatever you want. The Sun is spewing out a massive amount of radiation energy in all directions all the time...what a waste! Eventually we should be able to effectively black out the sun on all vectors apart from inhabited planets via perfect absorption. It's not infinite, but it's a lot more than what the Earth could ever hope to contain, and could easily support a certain figure of humans until it dies. The stars and laws of physics will be doing all of the work, so humans don't have to - in that sense, it's so cheap as to basically be free, but never technically. The cost may be as little as asking an AI to do something, and keeping the knowledge around of how it all works.
The point of the OP is not that everything should be free, it's that certain things that are necessary for life but very easy to now produce can be paid for by those who are motivated by peer pressure, if the land/manufacturing is productive enough. If only 10 people in a whole country are motivated by peer pressure and can't produce enough for everyone, then people will still be forced to work anyway and this is largely irrelevant. This is, incidentally, a major reason of why I believe communism failed (along with all the crazy). On the other hand, if 10 people working and 10 in training is all it takes to produce all the food/shelter/clothing/entertainment/all the wants of an entire planet, the OP is just a simpler system of organizing what's going to happen anyway.