Not sure why would you believe that.
Inside view: qualitative improvements LLMs made at scale took everyone by surprise; I don't think anyone understands them enough to make a convincing argument that LLMs have exhausted their potential.
Outside view: what local maximum? Wake me up when someone else makes a LLM comparable in performance to GPT-4. Right now, there is no local maximum. There's one model far ahead of the rest, and that model is actually below it's peak performance - side effect of OpenAI lobotomizing it with aggressive RLHF. The only thing remotely suggesting we shouldn't expect further improvements is... OpenAI saying they kinda want to try some other things, and (pinky swear!) aren't training GPT-4's successor.
> and the only way they're going to improve is by getting smaller and cheaper to run.
Meaning they'll be easier to chain. The next big leap could in fact be a bunch of compressed, power-efficient LLMs talking to each other. Possibly even managing their own deployment.
> They're still terrible at logical reasoning.
So is your unconscious / system 1 / gut feel. LLMs are less like one's whole mind, and much more like one's "inner voice". Logical skills aren't automatic, they're algorithmic. Who knows what is the limit of a design in which LLM as "system 1" operates a much larger, symbolic, algorithmic suite of "system 2" software? We're barely scratching the surface here.