But it isn’t. Every neuron runs the core circadian transcription-translation feedback oscillations. Every neuron is on a roughly 24 hour loop, synchronized by the master circadian oscillator, a clump of about 20k cells called the Suprachiasmatic nucleus.
The faster oscillations nest under that one, including the oscillations in firing rates.
Jet lag is when the synchrony and phase hierarchy breaks. Shift work does the same.
Now the brain doesn’t have a fast global clock like a chip. But that’s very much part of the evolutionary design. It’s not very energy efficient to have a fast global clock. And in a system like the brain, what purpose would it serve? In the brain, timing is information. You want the slow arrival of some signal to be slow so you can actually assign some meaning to it. A fast global clock would throw those gaps away.
In fact, there are neuromorphic and RACE logic chips that dump the global clock for the same efficiency reasons.