If writing is thinking then what happens if AI is doing the writing and reading?

And he was right. Poets and bard used to memorize entire epics. Writing changed this not by augmenting their abilities, but by changing expectations: it became acceptable to read form a written record, rather than from memory.

My memory gets exercised a lot less frequently than it would need to without writing.

But memory is also not thinking. It is a component in thinking, but it is not thinking itself. Discourse, arguably, though, whether in natural or symbolic language is thinking. If we offload all of that onto machines, we'll do less of it, and yes our expectations will change, but I actually think the scenario here is different than the one Socrates faced and that the stakes are slightly higher—and Socrates wasn't wrong, we just needed internal memory less than we thought once external memory became feasible, as cool and badass as it may seem to "own" Socrates in retrospect.

The thing is that we know because of writing that human memory is actually pretty awful and downright malleable. Even without attempts to tweak or optimize it, those epics would mutate over time and nobody would notice without a written reference.