your "ideal" of 7 seems invariant of size. surely the needs of the average ~x000 person company are completely different from Google.
CEO -> SVP -> VP -> Eng manager -> IC
Or, alternatively,
CEO -> Director -> Manager of managers -> Manager -> IC
I didn't feel like either needed more middle management (each had about ~2k employees), but in the case of the latter some reorganization would have helped (some managers had 50+ reports).