I absolutely agree with you that the current big LLMs enable an attack on all FOSS licenses and especially copyleft ones. That doesn't mean that one couldn't create LLM code generators in a respectful way. Do license analysis on the input code and then train separate models on the different license buckets, with the outputs from each model considered derivative works of the input corpus.
Also I don't think a restriction on the FSF's freedom 2 "The freedom to study how the program works" based on what tools you use and how you use them fits with FSF philosophy, nor do I think it is appropriate. You should be able to run whatever analysis tools you have available to study the program. Being able to ingest a program into a local LLM model and then ask questions about the codebase before you understand it yourself is valuable. Or aren't a programmer and or aren't familiar with the language used, then a local LLM could help you make the changes needed to add a new feature. In that situation LLMs can enable practical software freedom, for those who can't afford to pay/convince a programmer to make the changes they want.
https://www.gnu.org/philosophy/free-sw.html
In addition, OpenAI clearly do not respect copyrights and licenses in general, so would ignore any anti-AI clauses, which would make them ineffective and thus pointless. So, I think we should tackle the LLM problem through the law, and not through licenses. That is already happening with various caselaw in software, writing, artwork etc.
It isn't possible or practical to change the existing body of Free Software to use new anti-AI clauses anyway.https://juliareda.eu/2021/07/github-copilot-is-not-infringin...
BTW, LLMs could also in theory be used to licensewash proprietary software, see "Does free software benefit from ML models being derived works of training data?" by Matthew Garret:
https://mjg59.dreamwidth.org/57615.html