The most I've used AI for when it comes to RPGs is to generate a few phrases when creating a mechanical description. I don't trust it for narrative, or even to give me factual information. It is like a very well-trained monkey on a typewriter.

But, as much as I dislike AI, I also hate writing backstories. I always have, especially when I was young and all the roleplay I did was on free-form RP forums. I hate trying to fit a still-nebulous idea of a character into a socially expected amount of paragraphs or pages. Were I a less scrupulous individual, I might very well use AI to vomit something onto my character, simply to fill the space.

I guess it's all about expectations. I don't expect my players to make a long or detailed backstory (I'm fine with a few phrases, or just a general vibe), so there isn't that pressure to use AI in order to make something that's up to my standards. I'm sure you don't have huge requirements of your players in that regard, either, yet by putting a significant amount of focus on that aspect of their characters, it's not hard for a perceived necessity of "detailed backstory" to be constructed, even if it is an erroneous perspective. Apologies if you've already considered this point, though.

The use of AI as a shortcut, of course, ties back to psychology and reward systems and things of that nature (something, something, operant conditioning). No one is born knowing how to use AI to do their tasks for them, yet it becomes preferential to use it because it has such a low barrier to entry. Almost all progress or creation begets some form of suffering, if you consider things in their most abstract sense. It would be time consuming to write a backstory by oneself. Someone might be embarrassed by having to ask someone else to do this work for them, or if they present something that wasn't sufficiently dense. Yet the cost of using AI is primarily just the shame of cutting corners (a negative that depends greatly on one's own morals/ethics). I think until it becomes more socially acceptable to shame people for using AI in these types of tasks, it's just best to specifically ban it from one's tables.