Considering there are "GPT plagiarism" checkers, I don't think this will become an issue. I wonder at which point an extension will come out that will check a page's text if it was written by a human.
Those checkers already have a significant failure rate of false positives/negatives, and that will only get worse as LLMs come closer to human output. Note also that a checker can in principle never outwit a state-of-the-art AI, because the AI can just incorporate and therefore preempt the checker logic.
