Watermarking [0] is a better solution. It still works after changes made to the generated output, and anyone can independently check for a watermark. Computerphile did a video on it [1].
But of course, watermarking or checksums stop working once the general public runs LLMs on personal computers. And it's only a matter of time before that happens.
So in the long run, we have three options:
1. take away control from the users over their personal computers with 'AI DRM' (I strongly oppose this option), or
2. legislate: legally require a disclosure for each text on how it was created, or
3. stop assuming that texts are written by humans, and accept that often we will not know how it was created
[0]: Kirchenbauer, J., Geiping, J., Wen, Y., Katz, J., Miers, I., & Goldstein, T. (2023). A watermark for large language models. arXiv preprint arXiv:2301.10226. Online: https://arxiv.org/pdf/2301.10226.pdf