OpenAI is evaluating a technical solution to this problem by watermarking the output with small amounts of randomness, such that a series of tokens of output can be tested for having these small random variations.
Before they finish, someone else will have released a public access model that works just as well with no technical restrictions.
Worse still - it will be technically much easier to create something that modifies the output of the text generated by OpenAI's model without changing its meaning to defeat this. I think existing open source models can be adapted to do this already without too much work.