Yeah, I was using the non-adaptive brain as a baseline reducto ad absurdum. Obviously, it's possible to do better - the computing power wasted in the above design would be monumental, and the human brain is not such a model of efficiency that I don't think you can do better by throwing a few extra orders of magnitude at it. But it's something that even an AI skeptic should recognize as a possibility.
If we're going to be picky, also the idea that only neurons are relevant isn't right; if you replaced each neuron with a neuron-analog (a chip or a neuron-emulation-in-software or something else) but didn't also replace the non-neuron parts of the cognitive system that mediate neuronal function, you wouldn't have a working cognitive system.
But this is a minor quibble; you could replace "neuron" with "cell" or some similar word to steelman your point.
While writing my article "Could Robots Take All Our Jobs?: A Philosophical Perspective" I came across a lot of people who claim (roughly) that human intelligence isn't Turing computable. At one point this led me to tweet something to the effect of, "where are the sophisticated AI critics who claim the problem of AI is NP-complete?" But that was just me being whimsical; I was mostly not-serious.
A couple times, though, I've heard people suggest something to the effect that maybe we will need quantum computing to do human-level AI, though so far I've never heard this from an academic, only interested amateurs (though ones with some real computing knowledge). Who else here has encountered this? Does anyone know of any academics who adopt this point of view? Answers to the latter question especially could be valuable for doing article version 2.0.
Edit: This very brief query may have given the impression that I'm more sympathetic to the "AI requires QC" idea than I actually am; see my response to gwern below.