> or (more pointedly) that brain activity could not possibly implement cognition because it can be described as a collection of neural firings.

This sounds like a dismissal of the argument through a characterized straw man.

That is, it seems that reducing the complexity of the brain to "collection of neural firings" is not being honest about everything involved to a much greater degree than saying neural networks are a "collection of statistical calculations".

I too believe LLM's will grow in complexity, but presently I can not even fathom how they can be compared to the complexity of a system such as the human brain.