That's an interesting question, and something I've given thought to recently because of all the fuss about AI-generated content.
There is going to be some societal pushback and economic upheaval in creative sectors due to this. It's unfortunate for people in creative jobs, but technological progress has often (maybe always) come at the cost of periods of societal and economic tension.
As for the content itself, I'm a fan of the ease AI can bring to creative pursuits. While I do enjoy being creative, sometimes I'd just like to see a story idea written out so that I can read it, instead of necessarily being the one to write it myself.
AI stories aren't necessarily up to par just yet, but they will get there.
As for this site, if someone wants to post AI-generated stories, I don't see a problem with it. However, I would suggest that the beginning of the post have a note saying "This post [or this story] was generated by AI."
If someone wants to add an AI-generated post to an existing story that someone else had started, that might be iffier territory. AI isn't always great at storytelling just yet, plus the collaborative elements of this forum are meant to be about actual people writing together, not just generating AI stories. So I would check with someone before adding an AI-generated post to a story they started.
For example, on NeS3D (The Never-ending Story Thread 3-D), the fun there is about multiple people building off each other. Perhaps an AI post or two could be introduced as an experiment, but I don't think it should become the norm for that thread.
I'll echo many of Al's sentiments, but not all of them. Specifically, when it comes to NeS, I think an "A.I. author" could work out well in a number of ways: highlighting and/or subverting patterns most human authors wouldn't consider, help push things along when it seems the story is in a slump, and assisting a human author if it was "co-written" in ways perhaps more approachable than if it was done with another human author. With that said, just as I think NeS isn't as strong when it's dominated by any one human author, it would also suffer if it became dominated by A.I.-generated posts, or at least from the same A.I. if it's discovered different A.I.s might produce different results unique to them. Then again, I wrote a robot character into NeS, and I wonder if perhaps true A.I. will become a reality in my lifetime, and the implications that would bring, so I carry a bias in that regard.
In general, though, it's currently another tool, one that has the potential to bring both new creative heights and trouble for artists as they currently are, and it's a tool that's rapidly advancing, so addressing the challenges in a timely manner may be difficult. For this site, I'd certainly be interested in seeing how they could be used, though I definitely agree with Al that anything that includes the use of A.I. should be noted as such, since it is a very powerful tool that should be credited as such. I also definitely would hope that such use wouldn't be at the cost of diminishing collaboration between writers either.