My guess as an amateur neuroscientist is that what we call intelligence is just a 'measurement' of problem solving ability in different domains. Can be emotional, spatial, motor, reasoning, etc etc.
There is no special sauce in our brain. And we know how much compute there is in our brain– So we can roughly estimate when we'll hit that with these 'LLMs'.
Language is important in a human brain development as well. Kids who grow up deaf grow up vastly less intelligent unless they learn sign language. Language allow us to process complex concepts that our brain can learn to solve, without having to be in those complex environments.
So in hindsight, it's easy to see why it took a language model to be able to solve general tasks and other types deep learning networks couldn't.
I don't really see any limits on these models.
