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.
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.