But many of the examples you give actually accentuate that it is a hierarchy--either because the structure is computing movement across layers/ reference frames, or because the region (like thalamus) is highly modular, so mirrors the hierarchy.

I am guessing that one thing that may be inspiring these ideas is that our attention/awareness/consciousness can move flexibly between modalities, reference frames, etc, suggesting a kind of "flat" integrator. That's where things get very interesting (imho).