It goes in cycles. I remember the last time G did this (2006?) they had the 7 rule:
No manager with more then 7 reports No IC with more then 7 managers between them and CEO
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7 people with one manager seems fine. It could go up to 10 maybe, but that's just my own vibes.
7 layers thick of management feels like too much to me. You'll get a company full of professional middle management who's jockeying define the company culture and strategy. Is that the point? Vibes seem off though.
Is there a more scientific approach?
Yeah, so having more than that was banned. They didn't say you need 7 people between employee and CEO, just that there shouldn't be more than 7 people between them.
When you ban something you want to allow reasonable levels so you take a reasonable level, pad a bit, and ban that unreasonable level, so you agree.
But, also note for large companies, like 100k people, you need around that many layers or managers will have too many people to manage each.