This is information-theoretically guaranteed to make LLM output worse.

My reasoning is simple: the only way to watermark text is to inject some relatively low-entropy signal into it, which can be detected later. This has to a) work for "all" output for some values of all, and b) have a low false positive rate on the detection side. The amount of signal involved cannot be subtle, for this reason.

That signal has a subtractive effect on the predictive-output signal. The entropy of the output is fixed by the entropy of natural language, so this is a zero-sum game: the watermark signal will remove fidelity from the predictive output.

This is impossible to avoid or fix.