Is it necessarily the case that you could discern general intelligence via a test with fixed structure, known to all parties in advance, carried out via a synthesized monotone voice? I'm not saying "you definitely can't do that" just that I don't see why we should a priori assume it to be possible.
Now that likely seems largely irrelevant and out in the weeds and normally I would feel that way. But if you're going to suppose that we can't cleanly differentiate LLMs from humans then it becomes important to ask if that's a consequence of the LLMs actually exhibiting what we would consider general intelligence versus an inherent limitation of the modality in which the interactions are taking place.
Personally I think it's far more likely that we just don't have very good tests yet, that our working definition of "general intelligence" (as well as just "intelligence") isn't all that great yet, and that in the end many humans who we consider to exhibit a reasonable level of such will nonetheless fail to pass tests that are based solely on an isolated exchange of natural language.
Note that functional illiteracy is not some niche phenomenon, it's a huge problem in many school systems. In my own country (Romania), while the rate of illiteracy is something like <1% of the populace, the rate of functional illiteracy is estimated to be as high as 45% of those finishing school.
I don't mean to claim that it isn't possible, just that I'm not clear why we should assume that it is or that there would be an obvious way of going about it.