It's way out of my area of expertise, but my suspicion is that all these 4-12 Hz waves bouncing around in a 3D structure may be interfering to produce signals that tick much faster, and some functionality of the brain is clocked on that.

There's this thing called "scissor effect", where when you have two wavefronts colliding at an angle, you get an apparent wave that moves much faster than either of the input waves - if you do that with light, you can trivially exceed the speed of light. Now this isn't an information-carrying wave, but I believe you can still use this phenomenon as a "virtual clock", to synchronize a bunch of independent receivers to act on a frequency faster than the real, interfering clock signals.

Well, that, or the brain is just such a mess that it acts as a spread-spectrum source and none of the high frequencies are above the noise floor.

EDIT: and of course a little background research after writing this comment revealed it's already settled (through more invasive probing) that the human brain has elements operating in kilohertz range - the mystery isn't whether this happens, but how it adds up to cognition and consciousness.

There are faster waves than that, but the brain just doesn't seem to be fully synchronous. It doesn't have to have a fast "clock tree" if a lot of the low timescale activity is inherently async.

It's not at all how humans build computational devices. But humans run digital signals at gigahertz rates and do intelligent design. Nature doesn't do either.

I suspect that there are numerous advantages to silicon computation that biological neurons can't touch, but the brain is no slouch either - it was optimized for millions of years to be good for what it does. It's very good at what it does - sometimes because of, and sometimes despite its architecture.

It's honestly amazing that the brain even works as well as it does, given how slow neurons are. I suspect that distributed population coding that seems to be endemic to neural networks can also serve as a workaround for neurons being unreliable, slow to recover and subject to fatigue.

Seems to be pretty much in line with human reaction times?

I wouldn't be so sure that the brain necessarily clocks faster than that. I think it's more likely that faster chains of thought are defined by the flow of the waves rather than their frequency.