We can write new laws when new things happen, not everything has to circle back to copyright, a concept invented in the 1700s to protect printers' guilds.
Copyright is about granting exclusive rights - maybe there's an argument to be had about granting a person rights of an AI tool's output when "used with supervision and intent", but I see very little sense in granting them any exclusive rights over a possibly incredibly vast amount of AI-generated output that they had no hand whatsoever in producing.