Why would nothing get done? Does an automated economy need a bunch of people doing things?on a practical level it wouldnt work.
IRL 90% of the federation would be benefit scroungers and nothing would get done
In just thirty or forty years, I doubt much more than 10% of us will be able to really participate in the economy. It's far more a question of how society will react to the logical endpoint of the automation revolution, than whether it will happen at all.
Roddenberry envisioned a freeloader society with an elite 10% actually doing valuable work that couldn't be automated. No matter how many sour grapes as folks like to crush regarding the subject, perhaps because they've had to "work" all their lives and feel cheated--one wonders if their serf ancestors felt the same way about work today, when they weren't too busy dying of diptheria--the only plausible alternative is far drearier than a bunch of hippies enjoying their holodeck. That alternative being, of course, a social darwinist wonderland probably eventually resulting in massive human dieback.