To torture your analogy: in my mind, if the brain is like a bird, then modern approaches to machine learning are like helicopters. Yes, these things can both fly, but they don't fly in nearly the same way, and if your helicopter isn't getting off the ground then looking at the design of a bird isn't going to help you very much with many of the challenges you're going to face in getting it to work. You wouldn't claim that a helicopter is bird-shaped, even though there's some basic relationships between the aerodynamic principles of a bird's wings and a helicopter rotor.
If we're having trouble getting our helicopter to work, maybe we should be trying to make a working airplane first, since then we can base more of it off the design of a bird and use this to help us to better understand the basic principles of aerodynamics.
To be clear, once we understand the principles behind the neocortex, only then it will make sense to ask questions about the importance of oscillations or how it relates to asynchronous vs synchronous systems, and many more phenomenon we have observed but do not really understand.
Without an underlying theory to tie it all together, it's difficult to make sense of it.
I personally think that oscillations are more likely to be an emergent property which is a common theme in nature.
If we're having trouble getting our helicopter to work, maybe we should be trying to make a working airplane first, since then we can base more of it off the design of a bird and use this to help us to better understand the basic principles of aerodynamics.
Do you get where I'm coming from here?