The same oversimplification could have been made of the visual system before we became aware of specialized cortical units and their federated/hierarchical arrangement.
In time I suspect we'll yet discover that much of the brain is inhomogeneous in unexpected ways and peculiarly interconnected. If it were not, we'd understand more about how it works by now.
I feel like this is a bit of a false dichotomy. We've never encountered any spooky non-mechanical non-physical part of the brain, and we've been looking since Cartesian dualism was in vogue.
What we think of as human consciousness is likely just a bunch of feedback loops allowing the brain to analyze some of its own state as if it were an external entity.