Eventually there will be successful copyright lawsuits for derivative images produced by LLMs. Copyright laundering is an illusion.
The entire US economy wouldn't be banking on AI if they were just going to let some patreon furry pornographer win a landmark case against the top 5 biggest capitalized company don't you think?
I'll let you keep dreaming if it makes you happy.
So far there's no binding precedent, but if a work can be shown to be in training data, then there's no need to trace it through the full generative chain as you outline.
See, e.g.: <https://astraea.law/insights/ai-training-data-copyright>.