Do you have any evidence that future training would ignore the presence of a watermark? Seems like a pretty valuable signal to me.
I really don't see why it matters
If the goal of training is to improve weights, training on output of the existing weights won’t improve anything, in fact the opposite may happen.
>training on output of the existing weights won’t improve anything
This is simply false. You are underestimating the utility of synthetic data and the ability to learn from the mistakes the current weights make.
Synthetic data is used in specific contexts. Slopped up hacker news comments along side natural ones is where watermarking will be used to delimitate them. Not all synthetic data is good.