It is absolutely a fallacy, correctly called the "Luddite fallacy," and it isn't so much an economic fallacy as a logical one. The underlying mistake is to view jobs as an end in themselves. A job is a task that people want done so much that they are willing to pay for it. A society with no jobs is - by definition - a society where NOTHING NEEDS DOING because that society is so incredibly efficient that EVERY NEED ANYONE HAS IS ALREADY SATISFIED. Needless to say, such a society would be paradise.
Even just getting close to that situation looks like this: your life is already pretty great, you can get your basic needs and a whole lot more met by working only a few hours a week, even at very low wages since everything is incredibly cheap thanks to the efficiency of automation. If you can't work at all, everyone else is so rich and stuff is so cheap that their proverbial coins in your tin are already enough to live better than the average American does today.
Need I carry on? In a free market where working is not prohibited in any way, a lack of jobs is a lack of unfulfilled needs, which is a utopia. The absolute opposite of people being "left in the dust." They're instead left wanting for nothing. Of course in the real world there are always more "last 1%" services people want provided. If my life is already near perfect, I'd pay people a nice wage just to identify tiny itches on my body and scratch them so I don't have to take my hands away from the keyboard while writing posts. We'll realistically never run out of things to employ people for, and if we did that means we are in heaven.
No solution is needed to this "problem," and the poll is a false dichotomy. The solution is to let it happen, kick back, and enjoy sipping margaritas on the beach while robots do (almost) all the work for you.
Just imagine on a island with only 2 people A and B. If A have super high efficiency and can produce anything they need, then it seems that the other one B don't need to work at all
But who receive the ownership of those products usually can decide how to use it. So if A is making all the production, he has the right to keep everything, thus B will starve. B's survival purely depends on A and A might keep B living but give him only enough to keep his life
Someone will argue that B can make his own living by work by himself, but after A became very rich, he already bought all the land on the island thus B have to pay A rent. B's miserable production have to be given to A to pay his rent, but since A already have everything, he accept B's product just as a symbolic payment (He don't need B's product anyway), just to keep B alive
That's what happened in reality. In order to counter this inevitable result, since last century, government established social security to protect the people who already lost the possibility to make a living by their own: A were taxed and part of his production were re-allocated to B, but that process still don't change the nature of unemployment which is caused by A's super high productivity
Basically put, you can not violate the ownership, that will punish the motivation of honest working. But if you respect each one's work, some of the people will become super rich and some others will lose everything, to its root, this is caused by each people's different personality