The concern related to copyright is not that the AI labs would assert copyright over the code produced by their LLMs - that is a complete strawman.
The concern instead is that LLMs and all of their outputs may be found to be derivative works of their entire training set, and thus rendered unusable (as the training set is not distirbutable under any license).
I think this ship has long sailed and no court is going to dare give such a decision given the money involved, for better or for worse. But it's a much more realistic scenario, in principle, than LLM labs going mad and attacking their own customers.
Edit to add: there is another, completely different, copyright risk associated with LLMs - and one that is much more realistic. It is the fact that code generated by LLMs may not, in fact, be copyrightable at all. Which would mean that it can't be subject to the GPL. As long as it remains a minority of GCC code, this wouldn't matter much, but it could in time lead to significant portions of GCC becoming public domain, and thus cooyable, modifiable, and redistrubutable without providing the four freedoms.
Courts have already set a precedent on this (it's fair use) and even if these decisions were overturned, the liability would fall on the LLM creators for the initial training, not on their users. The outputs would keep being treated individually on their own merits.
In many timelines, non-copyrightable code in GPL project doesn’t restrict the user’s freedom, since an LLM can easily reimplement the functionality clean-room. AI has brought levels of freedom to users that GNU could never do. Practical levels of freedom, leading to real, positive outcomes. Software is finally free in the real world.
The mental model of slow decay into copyable is complicated. The code base is already a wash with contributions that have low copyrightability in US case law anyway, things derived directly from external architecture or documentation in barely novel ways, common system interfaces, and so on. LLM output is another output of this kind of class and sure sometimes large contributions happen that seem more significant, but they likely have little bearing on the work as a whole given it's earlier design provenance (at least for established and massive projects like this).
What is likely to get more muddy over time is the accuracy of any copyright registration, and the enforcement of copyright infringements on portions of the whole. These are already complicated cases and definitely so for compilers with so much "scènes à faire".
It's not clear how much this has a negative impact on cases around the whole, which tend to be the more important cases for the four freedoms that, while they have other intentions, have a primary intention of ensuring that the whole continues to be available for redistribution and extension in perpetuity.
I do not think that there is a clear link between these two areas at all, and the GPL's most important intents may be far safer long term than concerns of dilution suggest.