But it's all very interpolation/summarization-focused.
A "song lyrics in the style of Taylor Swift" isn't an actual song by Taylor Swift.
A summary of the history of Texas isn't actually vetted by any historian to ensure accuracy.
The answer to a math problem may not be correct.
To me, those things don't qualify as "new data." They aren't suitable for future training as-is. Sometimes for a simple reason: they aren't facts, using the dictionary "facts and statistics collected together for reference or analysis" definition of data. So very simply "not new data."
Sometimes in a blurrier way - the song lyrics, for instance, could be touching, or poignant, or "true" in a Keats sense[0] - but if the internet gets full of GPT-dreams and future models are trained on that, you could slide down further and further into an uncanny valley, especially since most of the time you don't get one of those amazing poignant ones. Most of the time I've gotten something bland.
[0] "What the imagination seizes as beauty must be truth"