right up until they can
Absolutely, this right here. Except they haven't yet. So one day they will be at genius level. But this is not that day. Maybe literally tomorrow? More likely LLMs will never be sufficient on their own, at least in the more neural network sense, and probably in the near future a more mathematical & counting functionality will be grafted onto the LLM, so that a question like "what is 1+1" will at least have awareness of the fact that computationally speaking the answer would be 2, even if the actual answer given is something else, like "little Bobby, you told me that you would consent to going to bed in 10 minutes... but that was 25 minutes ago, and you asked me to do just one more... and we did five more" - you know, true AGI stuff.
Which when it comes will be astonishing. But for now it makes astonishing mistakes, yet techbros want all of the water and electricity and to keep the profits while off-loading all the costs to society at large now, even though the remotest possibility of a true AGI has yet to be demonstrated can come from an LLM - especially alone without other counterbalancing components.
I don't trust anyone who calls these theorem-proving models as "geniuses", senile or otherwise. An LLM yes, an "AI" very much controversially (where the outcome depends upon power and politics, not any kind of search for realism to represent Truth), an intriguing contribution definitely yes, an important one the jury is still our on how useful the result will ultimately be but I preemptively concede that it at least could be, but an AGI... can it do anything other than predict, based on its training data?
It can shuffle, mixing and matching existing things according to a weighted fashion and in a manner such that we humans may find the end product useful (at least sometimes, although a LOT ends up being discarded as well and that is something that I find missing from most discussions - e.g. if a googleplex of monkeys hammering away on a keyboard can produce a Shakespearian play, buried amongst googles of nonsense words, does that make the monkeys "smart"?), but can an LLM think? That is what the "I" stands for, after all?
At which point I've wrapped around to agreeing with you, not that we currently have an AGI bc I think we do not yet (definitely not a "genius" one, senile or otherwise), but that in order to even answer that we would have to know what that "I" even stands for in the first place. Critical thinking? Ability to count and do computations? Articulation of internal processes? And so on.