Benjamin Franklin famously taught himself to write well by doing what you describe: Read a piece of a book, then rewrite it, then compare.

At first his copies were badly degraded. Eventually, he was considered one of the best writers of his time.

I feel like there's probably some way "the copy is better" could be quantified (at least to the point where it fools most of the people most of the time). If so, then expect LLMs to learn the same trick within a generation or two.