What actually takes up space is the connectors for stackability. If there was no stacking, the hat would be 1/3 the size.
Edit: no, I didnt say it correctly: the hat uses a 2 $ bt module. That module sits between the stackable connectors. If a real PCB for the hat was made, so that we have BT chips on the reverse side in the free area, the connectors could be right on top of each other, and the hat could be a lot smaller -