The real question is whether we're worse off or better off overall than we were in Socrates' Athens.

Regardless of how you feel about this question, it doesn't necessarily map to the current situation.

Just because the loss of one skill to a supplanting technology led to one kind of societal change, does not mean that the loss of any skill to a supplanting technology will lead to the same kind of societal change. Assuming that to be true is a faulty generalization.

I think it wouldn't be hard to argue that writing has changed human society more profoundly than any other invention. Whether or not the change was positive is a matter of taste and likely unanswerable. The point though is there are plenty of other examples of new technologies that changed technology and deskilled humans, both mentally and physically, that changed society in radically different ways, compared to writing (looms, tractors, sails, calculators, computers, guns, and so on).

There's certainly a case to be made that, of major past technological advancements, the kind of deskilling we'd see due to heavy AI use is most comparable to the deskilling due to writing: presumably there were many day-to-day and essential activities that made use of the mental acuity people would lose due to reading, just as there are many day-to-day activities that one can imagine people becoming less skilled in due to AI use.

To me, the most dangerous difference though may be in what gets deskilled. If we only relinquish our ability to do certain menial and intellectual drudgery, that is one thing. But if what we actually relinquish and deskill is our agency and discernment, as a result of constant "delegation" to AI systems, I think we're in for a much worse time.

There's a distinction to be made between "worse off" and "worse". Socrates was arguing that writing-users would be worse as people, not that they would experience lives they didn't like as much.