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.

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.