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.