I can't quite agree with your framing of loops, balance, and rhythm. A lot of the output patterns produced by the cerebellum are singular actions: tying your shoe laces, for instance. Progressing from learning how to do that to struggling whenever you try to do it differently than you always do (start halfway, reverse directions, verbally describing what you're doing, etc.) is more indicative of the optimizations that are encoded in the cerebellum, imho.
I can certainly imagine AI architectures evolving similar dedicated circuitry to perform common computations. As in us, it might be particularly useful for applications where some form of motor control is required, such as in self-driving and robotics.
It's a bit harder to come up with areas beyond that where it makes sense for general AI. Math and physics spring to mind, but in general the tendency to snap to a certain handling of an input pattern might be way too limiting in terms of creativity; it might become narrow-minded and primitive in those areas. OTOH, again, that might be fantastic for narrow AI applications.
Pipes and cycles is a good way to think about it. Our brain has cycles and we have pipes that move information around: we're processing information to persist.
Some of the information we're aware of, some if it were not, and sometimes we want to be unaware, of certain things, when we're aware (bored).
Recently we learned there are 2 separate lines of development: 2 separate progenitor stem cells that lead to a fully developed front and hindbrain.
Cybernetics is about autonomous loops: there is a loop that keeps us alive. The loop iterates, has rhythm, cycles. There is information that has to be 'brought into a moment' to control your body and mind. And we need two systems to keep our stuff held together and give us a sense of self.
Whatever you think of a given moment: the electric order required to operate your body seems to break down to about an 80/20 ratio of processing power, brain material (a dual system in itself, with two halves) if you consider neuron count.
An 80/20 split to properly persist us and provide a 'now' experience that grows over time. We use the same system to imagine and predict.
Also: consider recall speed, and speed of information transmission itself. What is required for the brain to respond to input, or just persist the body? It's not only important to move information quickly, you just move the right information.
When writing? When riding a bike? Singing, sleeping, etc.
For any moment, like the singular moments you mentioned, we wrestle with boredom and recreation. And we balance time, work, etc. because we have basic needs that have to be met first. Your heart beat must be adequate, you need a certain amount of breath, sleep, food, etc.
It would be a lot of mental burden: try manual breathing and going about your day for as long as possible. The ratio of neurons is about 80/20 for some reason, and it must be a good one for us.
There is a lot of looping and control at play however 'aware' we are.
The cerebellum piping, the control, requires a lot of matter/piping, and the ratio is interesting. I'm considering a whole robotic thing: servos, and brains, and all the control that's required to balance input and output to 'do something', the keepalive loop for a robot that thinks and moves like us:
Bringing it back though, there's an outer loop that allows us to persist. For us it's two systems.
Our 'keepalive' loop two systems, 80/20 split.
is an outer control loop for robotics, like you're mentioning. Those pipes and cycles from the start of this message. If the goal is to create something that resembles a living creature that moves and responds to environment, and does work to persist:
I expect to see a repeated pattern again, the 80/20 ratio. 80 percent required for managing autonomous loops, and 20 percent to do 'creative thinking' or something else, simply because of the new 'dreaming RSI' news: new insights into automated improvement, another autonomous loop.
As we add more loops...the ratio might matter, depending on what you want to do. But if it's lifelike robotics, I expect to see the 80/20 split. But obviously we would just iteratively work out the optimal ratio based on economy.