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.