Note the way I expressed it, the emphasis is on contributing. Your particular spin strikes me as an eagerness to oppose a particular POV, then you go on to project that POV onto me. I don't thrive as well when contributing as a volunteer, which I did when under employed, as when I have a full time job. Keep in mind the efficient market hypothesis. Most of the jobs constituting valuable contributions are going to be paid. There are going to be exceptions, of course, but not all of those roles are going to be suitable for everybody.
Your analysis is fatally flawed from this point. Teachers are valuable, and I feel they should be full-on professionals paid like we pay coders. Farm Workers and Wait Staff could be valuable, depending on what level of skill, diligence, and expertise they bring. Those two categories cover a very broad range of levels of expertise.
Parents and caregivers didn't start out as a part of the economic system. They also don't necessarily have to be paid. It has been noted that paying people to do what they'd do for free often has well known pathologies associated with it.
This type of motivation is what leads impoverished South Americans to destroy the largest rainforest on Earth, or African children to work in gold mines exposed to toxic mercury, dragline fisherman to deplete great oceans full of life, the list is endless.
This only shows that our world has incentives that are sometimes way out of whack. It doesn't then follow that the answer is basic income. Other societies have tried "from each according to their ability, to each according to their needs" with following drops in productivity.
I find this interesting, because it's a great example of some of the values implicit in American society.
Note that the way you expressed it, essentially the only way to contribute to society is by working a job. I don't think it's a stretch to claim that that's a very narrow-minded way of looking at it.
In my opinion American society is really, really good at all things economic, but really, really bad at actually enjoying/finding value in the things that go on outside the office.