That makes complete sense. Also, the formulas for volume lead to the same conclusion, just in a more complicated way. In one that I can’t follow 
Hyperbolic space makes little sense for the structure of the Safe Network itself because it doesn’t form a scale-free network. The type of subdivision sections use is strictly Euclidean, for example. (I’m not sure how node-aging changed things though so maybe I’m a little wrong on some more subtle level.)
Social networks, various types of knowledge fit terribly in Euclidean space but comfortably in hyperbolic, and then they can be searched easier. Not only that, but it also makes graph sharding (something pretty hard) not only possible but also relatively simple:
This picture is from a paper about indexing and sharding a large spatial dataset using the Poincaré disk model of hyperbolic space, and they found in their simulations that the subsections end up with the same average number of entries.
Your profile picture makes it just a tiny bit obvious 
Yes, all of this makes sense for the Safe Network only if graphs get some sort of “first-class object” support from the network because I’m skeptical that a large-scale index could be kept up-to-date just on the client side.