Sigh... Every man knows the mechanisms of the mind are yet unlike the cogs and pinions of clockwork. It remains the machinery, the relation of spring and escapement, that is most relevant. Hitherto in human history, I think, such structure has not been described.
If you build a neural network out of cogs and pinions, sure.
Comparing the brain to most complex machines in history wasn't a mistake, any more than refining laws of physics were. Successive approximations.
And we're no longer at the point where we're just comparing brain to most complex machines. We have information theory now. We figured out computation, in form independent of physical medium used. So we're really trying to determine the computational model behind the brain, and one of the ways to do it is to implement some computational models in whatever is most convenient (usually software running on silicon), and see if it's similar. Slowly but surely, we're mapping and matching computational aspects of the brain. LLMs are just one recent case where we got a spectacularly good match.