That's the thing: we ripped the entire idea of learning connectionist networks straight out of the brain - but our implementation of that idea is very different.

The asynchronous nature of BNNs? The brain does that because its neurons are slow and synchronization is unnatural. The predictive Hebbian learning hybrid that the brain uses? Loses to backprop if you have what it takes to implement backprop.

There are a lot of mediocre or unapplicable ideas in the brain for every good one. Figuring out how the brain does the things it does is hard enough - but making use of that is even harder. It's why ANNs and BNNs diverge so much in form even as they converge in function.