The announcement of ChatGPT's ban only talks about the potential incorrect answers the AI could add to the site if allowed.
However, I can think of more uses for the AI than answers. You focused on answers, but a site's reputation can be hijacked by asking the AI to generate questions, for example.
I asked ChatGPT:
Can you generate a question for Stackoverflow?
Sure, here's a question:
"What's the best way to implement authentication and authorisation in a Node.js and React application using JWT?"
I asked too:
Can you generate a question for Stack Exchange Earth Science?
Sure! Here's a question:
"What is the relationship between ocean currents and climate change, and how do changes in ocean currents affect weather patterns?"
It only gives a title and doesn't generate a wrong code for Stack Overflow. However, the Earth Science question is good, and a user could hijack the reputation system by posting successive acceptable questions on the site.
Shouldn't the ChatGPT policy be more specific about where you can and can't use AI?
Does the policy apply to every Stack Exchange site, or should every site define its own policy?