There's long been a recommendation on SE sites that users only post questions that they genuinely want the answer to. See https://stackexchange.com/tour:
Real problems or questions that you’ve encountered
Using LLMs to generate questions purely for the purpose of increasing the amount of content on this site doesn't pass this test. I also suspect that users would be less likely to answer a question that they felt was generated by an AI because it gives a weaker sense that they're helping someone. That might increase the Q count on the site, but it would worsen the Q:A ratio.
A potential legitimate use case is where someone uses an LLM to rephrase a genuine question, particularly when English isn't their first language. A blanket ban on the use of LLMs as a tool might be an exclusionary policy, given that this currently doesn't appear to be a problem on ES.SE.
A more nuanced policy would be based around banning problem uses (e.g., content farming) and/or permitting narrow uses (e.g., improving your own question). It would be harder to police, but more equitable.