The real question is, what happens when the AI starts producing text outputs that are indistinguishable from a real person's post? That's already possible. If the person knows some basic English he can read the AI response and re-write the same thing using his own words but there will also be other, better "humanizer" tools out there. (they are already available as far as I know).
I think this is very well captured by theymos in the last paragraph of the AI guidelines.
You talked about reading AI responses and re-writing it using their own words. This should be a secondary concern, the primary concern should be how the AI got its prompt, what kind of prompt was given it. Was it a prompt to get an idea? if yes, it's fair but if it is a prompt of cluelessness asking AI to write a whole text, this will be disastrous.
However, theymos recommends against ever relying on AI writing advice very much.
You can use AI to suggest grammar/style improvements, or to give you ideas, with you manually implementing those suggestions; but avoid directly copying more than a few words from the AI. However, I recommend against ever relying on AI writing advice very much, since mixed in with its good suggestions it'll usually also give bad suggestions which will just erase all personality from your writing. Better your writing be flawed and authentically-you than "correct" but stripped of any soul.