If we go by "fool's errand" as "needless or profitless endeavor", https://arxiv.org/abs/2303.11156 may already be a good enough answer to the paper you cited, so their work is already laid out for them. The green token idea is thoroughly attacked with much more effective techniques than those in the original paper through "recursive paraphrasing". Among some hypotheses in the paper, one is particularly interesting:

>These experiments provide empirical evidence that more advanced LLMs can lead to smaller TV distances. Thus, based on Theorem 1, reliable AI text detection would become increasingly difficult