It’s not a licensing issue because OpenAI does not own the copyright to the output of GPT-4. The people who might have a copyright claim are: the authors of the training data, if there is a clear resemblance between the training data input and the output, and rarely the author of the prompt.

OpenAI could argue that because some of the training data was written by them, they have a copyright claim to the output. However, this is a very slippery slope for them as the entire existence of OpenAI is predicated their use of training data being fair use.

OpenAI can only control the output of GPT-4 via their terms of service. When you sign up to use ChatGPT or other services you agree to certain conditions.

This can thus be circumvented by an intermediary that happens to release the output somewhere. Since you don't need permission from the copyright owner to train models, you just.. take it from their website or something. As long as you don't accept their terms of service, there is nothing they can do.

Additionally, different jurisdictions take different views on browsewrap and clickwrap agreements. Usually terms of service regulate acceptable use of the website, don’t spam, don’t harass other users, don’t use bots, things that the website has a legitimate interest in.

Attempting to control what users do in their own time with public domain information from your website may be a step too far for a click or browse wrap ToS.