For the millionth time, piracy isn't theft. It's copyright violation, not copyright theft.
No, a reduction in traffic is not sufficient to conclude that a copyright violation has occurred. Sure, it might have. Alternatively it might have produced a lossy summary in which case the reduction in traffic raises some difficult questions about the value of the original work.
In other cases an LLM can synthesize a genuinely useful explanation of a subject that is precisely tailored to the needs of the asker. In those cases the machine output might well prove more useful to the asker than any single original reference would have.
For something like news where what you're paying for is timely delivery it makes sense to restrict automated (not just LLM) access for the first few days because a similarly timely summary will capture the majority of the value proposition of your service.
That's not typical though. For example, I'm certainly not going to be satisfied with a summary of the plot of a book I'm interested in. Would you want to watch a 10 minute highlights reel in place of a 2 hour feature length film?
For the millionth time, the reason we have copyright in the first place is to encourage creation of original creative works. This is clearly stated in the US constitution (and similar phrasing is found in the relevant legal texts of other jurisdictions).
You can apply obsolete legal tests that have been used to enforce this principle all day long, but the central question remains: Does generative AI encourage creation of original creative works?
If the answer is "no", which it clearly is, then whatever laws and legal tests exist to enforce IP rights need to be amended - or the constitution does.