It seems to have merit as a subdivision scheme.

The shapes look a bit wonky when projected onto a map, though, and it may not be as intuitive to reason about as the hexagons that would (mostly) result from subdividing an icosahedron. With a subdivided icosahedron you end up with a regular lattice of shapes that is easier to reason about. I think an icosahedron might be a better fit for an indexing scheme for that reason, despite it's higher mathematical error in approximating the sphere at a given resolution.

I explored a similar idea four or five years ago, without being aware of H3. My goal was to find a compact multi-resolution geospatial height map format. My idea was closer to H3 than to yours, it seems.