update There was a further change in policy (see link in OPs question or Karsten's answer). Originally the choice was to opt in to display a banner, of which there are two styles (so 3 choices altogether counting also the no-banner option), but now there are two choices, either displaying the more drastic
**Reminder**: Answers generated by artificial intelligence tools are not allowed on [Site Name]."
or the default
**Reminder**: Answers generated by artificial intelligence tools must be cited on [Site Name]."
Officially the justification for the default is the site-wide proper attribution clause of the Inauthentic Usage policy, according to the accepted answer. According to the policy, the use of AI violates the expectation that content was produced by a human.
I think it's more complicated. Content on SE comes with no guarantees whatsoever, so the question of attribution is primarily one of integrity (honesty), akin to not plagiarizing content. Attributing output to AI is different from regular attribution in that AI output is anonymous and untraceable to a particular person or text source. Attribution at best serves as a warning to readers that what they are about to read comes from a black box and might be nonsense.
Use or not of AI does not alter the burden of ensuring quality, which requires screening a post for accuracy, including material sourced from another site. And quality is in the OPs best interest to retain reputation. Quality is also enforced by a voting system which assigns rep ("vetting by a community of human readers").
In fact, vetting by the community complicates matters, because candid use of AI through attribution generally gets a negative reception, whether AI is allowed or not, to the detriment of an honest user. Moreover, incontrovertible detection of AI can be difficult, and attribution is complicated when AI might be used to edit only parts of a post. Finally, it is hard to justify banning incorporation of AI content that improves a post. In fact, AI should increment quality if the OP can tell a correct from an incorrect answer and does a reasonable editorial job (ie an incorrect answer is still worse than no answer). Bayesian logic says that a post is like a trial wavefunction: any additional vetted information should improve quality.
We could opt for a "don't ask, don't tell" option which officially bans use of AI, but where we pretend there is no such thing as AI. This is in fact close to my current policy. I keep my eyes open but don't fuss over AI.
But the need to choose a banner means we can't make this official policy.
Therefore I suggest officially banning AI use, since it reduces the likelihood of burdening the site, making exceptions for use in formatting, spell-checking, or assistance with translation. Quality remains the OPs responsibility.
General opinion on AI
AI is a tool, and like any its use should be judged based on intent and effect. Users should use it with caution, and in particular not post raw output from a chatbot such as ChatGPT.
Reasons include the purpose of answers on this site as expert-curated content. When you post an answer you should expect to vouch for accuracy by providing supporting statements (a logical exposition or supporting references). A chatbot does not provide references, is known to be often illogical, and cannot be held accountable for accuracy.
No one here can interfere with your use of AI to research an answer, or even to assist with writing text and formatting one. AI should however be used as a tool as might a web search engine. Ultimately the person posting should serve as a filter to ensure usefulness and accuracy.