I fully support network wide AI ban. A permanent one.
For now the most prominent issue with AI answers is that they are mostly incorrect. Because they look like well written elaborate answers they don't look like common low quality answers that are otherwise poorly written or just contain code snippet (on Stack Overflow).
Because of that they are harder to moderate - common flags like low quality and not and answer don't apply. Yes, incorrect answers could be downvoted, but that also requires some expertise in subject matter.
If the user posts plenty of such answers, they can also avoid answer ban, by getting upvotes from other users deceived by initial good impression.
Overall, incorrect AI generated answers are evidently harmful.
Why permanent ban?
If we take a look beyond incorrect answers, it will become clearer why permanent ban is necessary.
Let's say we allow users to post AI generated answers they will check for correctness (ignoring for the moment other potential issues mentioned in other answers).
User is an expert and can verify answer correctness
If the user has expertise to verify the correctness of an answer, then they also have the expertise to fully write one. Grammatical errors were never obstacle when answer content was otherwise good, and there is plenty of users that edit such answers, so improving language is not the advantage in this scenario. Also, there are other tools that can correct language errors.
Because users that have expertise, don't need AI, if we allow such answers to be posted, there would be extremely small amount of such answers as verifying the AI generated content would probably take more time than writing the answer.
We are not going to lose any good content posted and verified by the experts in such cases.
AI becomes so good it gives correct answers
This will probably never become true, but let's pretend that AI will generate if not always, then correct answers most of the time.
If this would be true, then people could just directly ask AI the question, instead of posting it on Stack Exchange. Similarly, currently people are supposed to read documentation and use Google or other search engines for solutions before simply asking questions.
We don't need to allow AI generated answers, if AI can directly solve the problem.
Another aspect why we need to permanently ban AI, is that AI didn't magically appeared. It is being trained on human generated content. Stack Exchange strives to quality, and we need to preserve human generated content to do that. If we allow AI answers, no matter how good they are, we will start losing experts willing to share their knowledge.
If you can post in few seconds what AI gave you, why would you bother adding original content. With time less, and less people will be motivated to participate, and at the end, Stack Exchange will become collection of AI generated posts nobody will read anyway because it would be much faster to ask AI directly.
And when you can effortlessly get virtual Internet points, they will lose value fast.