Why not switch it around? Solves problems of privacy (no data upload), is far more doable and it's far more important to be able to verify content has not been tampered with after originating from a human or capture device (like a camera). We also have decades of cryptographic experience in reliably signing text, images, video, etc. and it doesn't break apart because a text is too short.
Having proof that content (especially images and video evidence) is unmodified (whether via Photoshop, Paint or a model) is far more valuable then having evidence that an image was manipulated or generated fully by a model (which still leaves other forms of manipulation), I feel the same goes for human authored vs generated text. Free to admit that using models to generate any kind of media whole-cloth is still unappealing to me and I still pay for commissioned artwork or make it with my limited abilities for what that's worth. Do like to (poorly) write my musings too and see UX as something were thoughtful contributors (like the opinionated, sometimes controversial, but certainly talented GNOME Gitlab contributors) can make a major impact.
Code can be beautiful, interesting and serve purpose beyond execution, of course, but for most people, in most cases, it does not in the same way as audiovisual content (not limited to art). Having code just to execute and resolve a problem can have value all in itself, the code being a means to an end whose quality, let us be honest, was barely a concern in most corporations long before LLMs.
Also have rarely (honestly never) before LLMs fully owned all parts of any code base, always relied in part on someone's prior effort in (Flutter/Dart mostly) packages, whereas when writing, drawing, etc. I have far more situations where I make something from scratch and everything there is only there because of my conscious decision. Even simple marketing mockups that, quality wise, any modern model would beat feel different when I was fully in control, where to place what, etc. Objectively worse (at my skill level), probably, but still never the same.
Knowing something was made from scratch by a human has value to me, beyond misinformation prevention. Knowing for a fact that LLMs were used instead of importing a library, using a template, or something similar that leads to expending similar amounts of effort, I don't see that being nearly as valuable. Heck, with all the importing and my experience back then vs now, I am spending more effort actually fully reading any LLM output in my code then I spent back then auditing Flutter/Dart packages. Then again, LLM output fails far more unpredictable then those messy packages that simply got Gradle to take down my system...
Happy to admit, I have been skeptical of watermarking LLM output being feasible for quite some time and having looked into SynthID Text and proposals being researched, I am convinced that it is challenging to impossible beyond the lowest common denominator and less important then proofing human authorship.
It will catch people just copying LLM output into their replies without thought, which is not a negative in my book, especially if it is not discernibly affecting output quality in regular use cases. Anyone who wouldn't copy Wikipedia into their dissertation will, in my opinion, be able to bypass text watermarking as proposed however, I feel we need to be honest there.
Thing is, if that's the case and text watermarking will only ever catch LLM created slop, is that a bigger problem then the misinformation, harm to creators due to authorship questions and accusations, making it harder to use evidence in proceedings, teachers not trusting students even when they did the work themselves, etc.? Signatures for all such cases will be difficult to implement, yes, but I feel are going to be of greater value in the not to distant future and I equally feel are not impossible, not least because idiots will always want to hide their LLM usage, whereas human authorship is something they take pride in and want to proof.