Is the question easier to agree on if flipped around: What kind abilities or qualities should a (future) model exhibit to be considered of, say, average human intelligence?
I think perhaps the OP question (or the "flipped" question) is not really that interesting in regards to LLM's. Research (driven by whatever motive) will by all accounts drive LLM to be more and more likely to produce what most would consider output generated by an intelligence (i.e. a sort of "intelligence is in the eye of the beholder" measure) and the interesting question in that context seems more to be if this path of evolution will be "blocked" by some fundamental but so-far undiscovered mechanism or model structure.
Compare, if you will, with study of animal intelligence. Clearly the mere presence of a brain in an animal does not imply it is able to what we would classify as intelligence, but some animals (e.g. chimpanzees) are clearly able to exhibit intelligent or at least very adaptive behavior in their domain even if they cannot be trained to explain general relativity. In that context I guess my question becomes what set of mechanisms or structures in the human brain, compared to such an animal brain, makes it qualitatively more capable of intelligent behavior? Considering homo sapiens have a common evolutionary ancestor with every species on this planet then I can only see the significant difference be structure and scale of the brain. And if so, why shouldn't LLM's with the right size and structure not also be able to achieve human level intelligence via such an evolutionary path? I am not saying such a path is guaranteed to be found, more that such as path has already been shown to exist and be evolutionary reachable in the example of homo sapiens so why not also with LLM's as a starting point?
(I realize discussion of the level of intelligence exhibited by possible future models are not what the OP posed as question, but, just to repeat myself, since we have such trouble answering that question maybe it is more easier or relevant to discuss if there is anything fundamentally blocking current models to evolve to a point where everyone would agree yes, now the behavior is intelligent).