I do not think it is feasible to make sure prompts are reproducible. Considering that a LLMs are large you can not host every version of the model indefinitely.
Perhaps you would prefer to include the generated text source as an author.
It would however be nice to have a mode where any output that matches some existing text in the training set could be highlighted, to help one avoid unintentional plagiarism.
If so, we could pattern match historically, and discover the base rate of plagiarism.