It is most certainly a predicament. If people feel like they can freely post ChatGPT content, it adds enormous strain on making sure that the solution provided actually works. This then has to be done by moderators (with experience) or other users who land on the site. If it is the latter, people might get frustrated that answers are wrong, devaluing SO's value overall.
In a nutshell, allowing AI in its current iteration will create more problems when it comes to moderation, content quality, and the sanity of sites users - pretty much.
Quite a lot of variables to find common ground on this one, but I think StackOverflow should not allow AI content for the time being.